x^3-76*x^2-11*x+22=0 (уравнение)

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    Найду корень уравнения: x^3-76*x^2-11*x+22=0

    Решение

    Вы ввели [src]
     3       2                
    x  - 76*x  - 11*x + 22 = 0
    $$- 11 x + x^{3} - 76 x^{2} + 22 = 0$$
    График
    Быстрый ответ [src]
                     /                      1                       \     /       /                      1                       \                                                                         \                                                                         
              5809*re|----------------------------------------------|     |5809*im|----------------------------------------------|               /    /     ________\\                /    /     ________\\|               /    /     ________\\                /    /     ________\\
                     |                     _________________________|     |       |                     _________________________|               |    |24*\/ 464673 ||                |    |24*\/ 464673 |||               |    |24*\/ 464673 ||                |    |24*\/ 464673 ||
                     |/          ___\     /                ________ |     |       |/          ___\     /                ________ |               |atan|-------------||                |atan|-------------|||               |atan|-------------||                |atan|-------------||
                     ||  1   I*\/ 3 |    /  442441   8*I*\/ 464673  |     |       ||  1   I*\/ 3 |    /  442441   8*I*\/ 464673  |     ______    |    \    442441   /|     _______    |    \    442441   /||     ______    |    \    442441   /|     _______    |    \    442441   /|
                     ||- - - -------|*3 /   ------ + -------------- |     |       ||- - - -------|*3 /   ------ + -------------- |   \/ 5809 *sin|-------------------|   \/ 17427 *cos|-------------------||   \/ 5809 *cos|-------------------|   \/ 17427 *sin|-------------------|
         76          \\  2      2   / \/      27           9        /     |       \\  2      2   / \/      27           9        /               \         3         /                \         3         /|               \         3         /                \         3         /
    x1 = -- + ------------------------------------------------------- + I*|------------------------------------------------------- - --------------------------------- - ----------------------------------| - --------------------------------- + ----------------------------------
         3                               9                                \                           9                                              6                                   6                 /                   6                                   6                 
    $$x_{1} = - \frac{\sqrt{5809}}{6} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{24 \sqrt{464673}}{442441} \right )} \right )} + \frac{5809}{9} \Re{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{442441}{27} + \frac{8 i}{9} \sqrt{464673}}}\right)} + \frac{\sqrt{17427}}{6} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{24 \sqrt{464673}}{442441} \right )} \right )} + \frac{76}{3} + i \left(- \frac{\sqrt{17427}}{6} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{24 \sqrt{464673}}{442441} \right )} \right )} - \frac{\sqrt{5809}}{6} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{24 \sqrt{464673}}{442441} \right )} \right )} + \frac{5809}{9} \Im{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{442441}{27} + \frac{8 i}{9} \sqrt{464673}}}\right)}\right)$$
                     /                      1                       \     /       /                      1                       \                                                                         \                                                                         
              5809*re|----------------------------------------------|     |5809*im|----------------------------------------------|               /    /     ________\\                /    /     ________\\|               /    /     ________\\                /    /     ________\\
                     |                     _________________________|     |       |                     _________________________|               |    |24*\/ 464673 ||                |    |24*\/ 464673 |||               |    |24*\/ 464673 ||                |    |24*\/ 464673 ||
                     |/          ___\     /                ________ |     |       |/          ___\     /                ________ |               |atan|-------------||                |atan|-------------|||               |atan|-------------||                |atan|-------------||
                     ||  1   I*\/ 3 |    /  442441   8*I*\/ 464673  |     |       ||  1   I*\/ 3 |    /  442441   8*I*\/ 464673  |     ______    |    \    442441   /|     _______    |    \    442441   /||     ______    |    \    442441   /|     _______    |    \    442441   /|
                     ||- - + -------|*3 /   ------ + -------------- |     |       ||- - + -------|*3 /   ------ + -------------- |   \/ 5809 *sin|-------------------|   \/ 17427 *cos|-------------------||   \/ 5809 *cos|-------------------|   \/ 17427 *sin|-------------------|
         76          \\  2      2   / \/      27           9        /     |       \\  2      2   / \/      27           9        /               \         3         /                \         3         /|               \         3         /                \         3         /
    x2 = -- + ------------------------------------------------------- + I*|------------------------------------------------------- - --------------------------------- + ----------------------------------| - --------------------------------- - ----------------------------------
         3                               9                                \                           9                                              6                                   6                 /                   6                                   6                 
    $$x_{2} = \frac{5809}{9} \Re{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{442441}{27} + \frac{8 i}{9} \sqrt{464673}}}\right)} - \frac{\sqrt{5809}}{6} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{24 \sqrt{464673}}{442441} \right )} \right )} - \frac{\sqrt{17427}}{6} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{24 \sqrt{464673}}{442441} \right )} \right )} + \frac{76}{3} + i \left(\frac{5809}{9} \Im{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{442441}{27} + \frac{8 i}{9} \sqrt{464673}}}\right)} - \frac{\sqrt{5809}}{6} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{24 \sqrt{464673}}{442441} \right )} \right )} + \frac{\sqrt{17427}}{6} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{24 \sqrt{464673}}{442441} \right )} \right )}\right)$$
                   _________________________                                   
                  /                ________                                    
         76      /  442441   8*I*\/ 464673                   5809              
    x3 = -- + 3 /   ------ + --------------  + --------------------------------
         3    \/      27           9                  _________________________
                                                     /                ________ 
                                                    /  442441   8*I*\/ 464673  
                                               9*3 /   ------ + -------------- 
                                                 \/      27           9        
    $$x_{3} = \frac{76}{3} + \frac{5809}{9 \sqrt[3]{\frac{442441}{27} + \frac{8 i}{9} \sqrt{464673}}} + \sqrt[3]{\frac{442441}{27} + \frac{8 i}{9} \sqrt{464673}}$$
    Численный ответ [src]
    x1 = -0.612450034557 + 2.16840434497e-19*i
    x2 = 76.1406746288000
    x3 = 0.471775405803000
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