Произведение корней 3*x^2-32*sqrt(2*x)-22=0

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    Решение

    Сумма и произведение корней [src]
    сумма
                                                                                                             __________________________________________________________________________________________________________________________________________________________________________
                                                                                                            /              __________________________                                                                                                                                  
                                                                                                           /              /                  _______                                                                                                                                   
                                                                                                          /   176        /  2444480   4096*\/ 39526                    3872                                                             4096                                           
                                                                                                         /    --- - 2*3 /   ------- + --------------  - ---------------------------------- + ----------------------------------------------------------------------------------------- 
              _____________________________________________________________________________             /      9      \/      729          243                  __________________________               _____________________________________________________________________________ 
             /             __________________________                                                  /                                                       /                  _______               /             __________________________                                       
            /             /                  _______                                                  /                                                       /  2444480   4096*\/ 39526               /             /                  _______                                        
           /   88        /  2444480   4096*\/ 39526                    3872                          /                                                  81*3 /   ------- + --------------             /   88        /  2444480   4096*\/ 39526                    3872                 
          /    -- + 2*3 /   ------- + --------------  + ----------------------------------          /                                                      \/      729          243          9*      /    -- + 2*3 /   ------- + --------------  + ----------------------------------  
         /     9      \/      729          243                  __________________________         /                                                                                                /     9      \/      729          243                  __________________________  
        /                                                      /                  _______         /                                                                                                /                                                      /                  _______   
       /                                                      /  2444480   4096*\/ 39526         /                                                                                                /                                                      /  2444480   4096*\/ 39526    
      /                                                 81*3 /   ------- + --------------       /                                                                                                /                                                 81*3 /   ------- + --------------   
    \/                                                     \/      729          243           \/                                                                                               \/                                                     \/      729          243         
    --------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                               2                                                                                                                                          2                                                                                            
    $$\frac{\sqrt{- 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}} - \frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{176}{9} + \frac{4096}{9 \sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}}}{2} + \frac{\sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}{2}$$
    =
                                                                                                             __________________________________________________________________________________________________________________________________________________________________________
                                                                                                            /              __________________________                                                                                                                                  
                                                                                                           /              /                  _______                                                                                                                                   
                                                                                                          /   176        /  2444480   4096*\/ 39526                    3872                                                             4096                                           
                                                                                                         /    --- - 2*3 /   ------- + --------------  - ---------------------------------- + ----------------------------------------------------------------------------------------- 
              _____________________________________________________________________________             /      9      \/      729          243                  __________________________               _____________________________________________________________________________ 
             /             __________________________                                                  /                                                       /                  _______               /             __________________________                                       
            /             /                  _______                                                  /                                                       /  2444480   4096*\/ 39526               /             /                  _______                                        
           /   88        /  2444480   4096*\/ 39526                    3872                          /                                                  81*3 /   ------- + --------------             /   88        /  2444480   4096*\/ 39526                    3872                 
          /    -- + 2*3 /   ------- + --------------  + ----------------------------------          /                                                      \/      729          243          9*      /    -- + 2*3 /   ------- + --------------  + ----------------------------------  
         /     9      \/      729          243                  __________________________         /                                                                                                /     9      \/      729          243                  __________________________  
        /                                                      /                  _______         /                                                                                                /                                                      /                  _______   
       /                                                      /  2444480   4096*\/ 39526         /                                                                                                /                                                      /  2444480   4096*\/ 39526    
      /                                                 81*3 /   ------- + --------------       /                                                                                                /                                                 81*3 /   ------- + --------------   
    \/                                                     \/      729          243           \/                                                                                               \/                                                     \/      729          243         
    --------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                               2                                                                                                                                          2                                                                                            
    $$\frac{\sqrt{- 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}} - \frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{176}{9} + \frac{4096}{9 \sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}}}{2} + \frac{\sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}{2}$$
    произведение
                                                                                                             __________________________________________________________________________________________________________________________________________________________________________
                                                                                                            /              __________________________                                                                                                                                  
                                                                                                           /              /                  _______                                                                                                                                   
                                                                                                          /   176        /  2444480   4096*\/ 39526                    3872                                                             4096                                           
                                                                                                         /    --- - 2*3 /   ------- + --------------  - ---------------------------------- + ----------------------------------------------------------------------------------------- 
              _____________________________________________________________________________             /      9      \/      729          243                  __________________________               _____________________________________________________________________________ 
             /             __________________________                                                  /                                                       /                  _______               /             __________________________                                       
            /             /                  _______                                                  /                                                       /  2444480   4096*\/ 39526               /             /                  _______                                        
           /   88        /  2444480   4096*\/ 39526                    3872                          /                                                  81*3 /   ------- + --------------             /   88        /  2444480   4096*\/ 39526                    3872                 
          /    -- + 2*3 /   ------- + --------------  + ----------------------------------          /                                                      \/      729          243          9*      /    -- + 2*3 /   ------- + --------------  + ----------------------------------  
         /     9      \/      729          243                  __________________________         /                                                                                                /     9      \/      729          243                  __________________________  
        /                                                      /                  _______         /                                                                                                /                                                      /                  _______   
       /                                                      /  2444480   4096*\/ 39526         /                                                                                                /                                                      /  2444480   4096*\/ 39526    
      /                                                 81*3 /   ------- + --------------       /                                                                                                /                                                 81*3 /   ------- + --------------   
    \/                                                     \/      729          243           \/                                                                                               \/                                                     \/      729          243         
    --------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                               2                                                                                                                                          2                                                                                            
    $$\frac{\sqrt{- 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}} - \frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{176}{9} + \frac{4096}{9 \sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}}}{2} + \frac{\sqrt{\frac{3872}{81 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}} + \frac{88}{9} + 2 \sqrt[3]{\frac{4096 \sqrt{39526}}{243} + \frac{2444480}{729}}}}{2}$$
    =
          /                                                                               _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________\
          |                                                                    3/4       /           ____________________________________________________________________                                              ____________________________________________________________________                                                              |
          |/         _______________________ /        _______________________\\         /           /          _______________________ /        _______________________\                 _______________________      /          _______________________ /        _______________________\     _______________________ /        _______________________\ |
      ___ ||      3 /               _______  |     3 /               _______ ||        /           /        3 /               _______  |     3 /               _______ |          ___   /               _______      /        3 /               _______  |     3 /               _______ |  3 /               _______  |     3 /               _______ | |
    \/ 2 *\\121 + \/  38195 + 192*\/ 39526  *\11 + \/  38195 + 192*\/ 39526  //    + \/    - 121*\/   121 + \/  38195 + 192*\/ 39526  *\11 + \/  38195 + 192*\/ 39526  /  + 384*\/ 2 *\/  38195 + 192*\/ 39526   + \/   121 + \/  38195 + 192*\/ 39526  *\11 + \/  38195 + 192*\/ 39526  / *\/  38195 + 192*\/ 39526  *\22 - \/  38195 + 192*\/ 39526  / /
    ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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                                                                                                                                 /          _______________________ /        _______________________\     _______________________                                                                                                                         
                                                                                                                              4 /        3 /               _______  |     3 /               _______ |  6 /               _______                                                                                                                          
                                                                                                                            3*\/   121 + \/  38195 + 192*\/ 39526  *\11 + \/  38195 + 192*\/ 39526  / *\/  38195 + 192*\/ 39526                                                                                                                           
    $$\frac{\sqrt{2} \left(\sqrt{\left(22 - \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt{121 + \left(11 + \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt[3]{192 \sqrt{39526} + 38195}} \sqrt[3]{192 \sqrt{39526} + 38195} - 121 \sqrt{121 + \left(11 + \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt[3]{192 \sqrt{39526} + 38195}} + 384 \sqrt{2} \sqrt{192 \sqrt{39526} + 38195}} + \left(121 + \left(11 + \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt[3]{192 \sqrt{39526} + 38195}\right)^{\frac{3}{4}}\right)}{3 \sqrt[4]{121 + \left(11 + \sqrt[3]{192 \sqrt{39526} + 38195}\right) \sqrt[3]{192 \sqrt{39526} + 38195}} \sqrt[6]{192 \sqrt{39526} + 38195}}$$
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