Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ 4*x^2+2*x+2*(24-x^2)^2+4*(24-x)еслиx=1/3

4*x^2+2*x+2*(24-x^2)^2+4*(24-x)еслиx=1/3 (упростите выражение)

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Примеры

Решение

Вы ввели [src]
                        2             
   2           /      2\              
4*x  + 2*x + 2*\24 - x /  + 4*(24 - x)
$$4 x^{2} + 2 x + 4 \cdot \left(24 - x\right) + 2 \left(24 - x^{2}\right)^{2}$$
Подстановка условия [src]
4*x^2 + 2*x + 2*(24 - x^2)^2 + 4*(24 - x) при x = 1/3
подставляем
                        2             
   2           /      2\              
4*x  + 2*x + 2*\24 - x /  + 4*(24 - x)
$$4 x^{2} + 2 x + 4 \cdot \left(24 - x\right) + 2 \left(24 - x^{2}\right)^{2}$$
           2            4
1248 - 92*x  - 2*x + 2*x
$$2 x^{4} - 92 x^{2} - 2 x + 1248$$
переменные
x = 1/3
$$x = \frac{1}{3}$$
               2                    4
1248 - 92*(1/3)  - 2*(1/3) + 2*(1/3)
$$2 (1/3)^{4} - 92 (1/3)^{2} - 2 (1/3) + 1248$$
          1              1 
1248 - 92*-- - 2*1/3 + 2*--
           2              4
          3              3
$$- \frac{92}{9} - \frac{2}{3} + \frac{2}{81} + 1248$$
100208
------
  81
$$\frac{100208}{81}$$
Степени [src]
                      2       
             /      2\       2
96 - 2*x + 2*\24 - x /  + 4*x
$$4 x^{2} - 2 x + 2 \left(24 - x^{2}\right)^{2} + 96$$
Численный ответ [src]
96.0 + 4.0*x^2 + 1152.0*(1 - 0.0416666666666667*x^2)^2 - 2.0*x
Рациональный знаменатель [src]
                      2       
             /      2\       2
96 - 2*x + 2*\24 - x /  + 4*x
$$4 x^{2} - 2 x + 2 \left(24 - x^{2}\right)^{2} + 96$$
                       2       
             /       2\       2
96 - 2*x + 2*\-24 + x /  + 4*x
$$4 x^{2} - 2 x + 2 \left(x^{2} - 24\right)^{2} + 96$$
Объединение рациональных выражений [src]
  /              2           \
  |     /      2\           2|
2*\48 + \24 - x /  - x + 2*x /
$$2 \cdot \left(2 x^{2} - x + \left(24 - x^{2}\right)^{2} + 48\right)$$
Общее упрощение [src]
           2            4
1248 - 92*x  - 2*x + 2*x
$$2 x^{4} - 92 x^{2} - 2 x + 1248$$
Собрать выражение [src]
                      2       
             /      2\       2
96 - 2*x + 2*\24 - x /  + 4*x
$$4 x^{2} - 2 x + 2 \left(24 - x^{2}\right)^{2} + 96$$
Общий знаменатель [src]
           2            4
1248 - 92*x  - 2*x + 2*x
$$2 x^{4} - 92 x^{2} - 2 x + 1248$$
Тригонометрическая часть [src]
                      2       
             /      2\       2
96 - 2*x + 2*\24 - x /  + 4*x
$$4 x^{2} - 2 x + 2 \left(24 - x^{2}\right)^{2} + 96$$
Комбинаторика [src]
           2            4
1248 - 92*x  - 2*x + 2*x
$$2 x^{4} - 92 x^{2} - 2 x + 1248$$
Разложение на множители [src]
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  |                                                                                                             /   184        /  1872043   I*\/ 4313836623                                                 2                                                                4802                | |                                                                                                               /   184        /  1872043   I*\/ 4313836623                                                 2                                                                4802                | |                  /   184        /  1872043   I*\/ 4313836623                                                 2                                                                4802                                                                                                             | |                                                                                                               /   184        /  1872043   I*\/ 4313836623                                                 2                                                                4802                |
  |                                                                                                            /    --- - 2*3 /   ------- + ----------------  - ------------------------------------------------------------------------------------------ - ----------------------------------- | |                                                                                                              /    --- - 2*3 /   ------- + ----------------  + ------------------------------------------------------------------------------------------ - ----------------------------------- | |                 /    --- - 2*3 /   ------- + ----------------  - ------------------------------------------------------------------------------------------ - -----------------------------------                                                                                              | |                                                                                                              /    --- - 2*3 /   ------- + ----------------  + ------------------------------------------------------------------------------------------ - ----------------------------------- |
  |              ________________________________________________________________________________             /      3      \/      432           144                     ________________________________________________________________________________          ____________________________ | |                ________________________________________________________________________________             /      3      \/      432           144                     ________________________________________________________________________________          ____________________________ | |                /      3      \/      432           144                     ________________________________________________________________________________          ____________________________              ________________________________________________________________________________| |                ________________________________________________________________________________             /      3      \/      432           144                     ________________________________________________________________________________          ____________________________ |
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  |            /             /               ____________                                                   /                                                           /             /               ____________                                                /  1872043   I*\/ 4313836623   | |              /             /               ____________                                                   /                                                           /             /               ____________                                                /  1872043   I*\/ 4313836623   | |              /                                                           /             /               ____________                                                /  1872043   I*\/ 4313836623              /             /               ____________                                        | |              /             /               ____________                                                   /                                                           /             /               ____________                                                /  1872043   I*\/ 4313836623   |
  |           /   92        /  1872043   I*\/ 4313836623                     4802                          /                                                           /   92        /  1872043   I*\/ 4313836623                     4802                   9*3 /   ------- + ----------------  | |             /   92        /  1872043   I*\/ 4313836623                     4802                          /                                                           /   92        /  1872043   I*\/ 4313836623                     4802                   9*3 /   ------- + ----------------  | |             /                                                           /   92        /  1872043   I*\/ 4313836623                     4802                   9*3 /   ------- + ----------------            /   92        /  1872043   I*\/ 4313836623                     4802                | |             /   92        /  1872043   I*\/ 4313836623                     4802                          /                                                           /   92        /  1872043   I*\/ 4313836623                     4802                   9*3 /   ------- + ----------------  |
  |          /    -- + 2*3 /   ------- + ----------------  + -----------------------------------          /                                                           /    -- + 2*3 /   ------- + ----------------  + -----------------------------------      \/      432           144         | |            /    -- + 2*3 /   ------- + ----------------  + -----------------------------------          /                                                           /    -- + 2*3 /   ------- + ----------------  + -----------------------------------      \/      432           144         | |            /                                                           /    -- + 2*3 /   ------- + ----------------  + -----------------------------------      \/      432           144                  /    -- + 2*3 /   ------- + ----------------  + ----------------------------------- | |            /    -- + 2*3 /   ------- + ----------------  + -----------------------------------          /                                                           /    -- + 2*3 /   ------- + ----------------  + -----------------------------------      \/      432           144         |
  |         /     3      \/      432           144                  ____________________________         /                                                           /     3      \/      432           144                  ____________________________                                        | |           /     3      \/      432           144                  ____________________________         /                                                           /     3      \/      432           144                  ____________________________                                        | |           /                                                           /     3      \/      432           144                  ____________________________                                                /     3      \/      432           144                  ____________________________ | |           /     3      \/      432           144                  ____________________________         /                                                           /     3      \/      432           144                  ____________________________                                        |
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  |       /                                                       /  1872043   I*\/ 4313836623         /                                                           /                                                       /  1872043   I*\/ 4313836623                                          | |         /                                                       /  1872043   I*\/ 4313836623         /                                                           /                                                       /  1872043   I*\/ 4313836623                                          | |         /                                                           /                                                       /  1872043   I*\/ 4313836623                                                /                                                       /  1872043   I*\/ 4313836623   | |         /                                                       /  1872043   I*\/ 4313836623         /                                                           /                                                       /  1872043   I*\/ 4313836623                                          |
  |      /                                                   9*3 /   ------- + ----------------       /                                                           /                                                   9*3 /   ------- + ----------------                                         | |        /                                                   9*3 /   ------- + ----------------       /                                                           /                                                   9*3 /   ------- + ----------------                                         | |        /                                                           /                                                   9*3 /   ------- + ----------------                                              /                                                   9*3 /   ------- + ----------------  | |        /                                                   9*3 /   ------- + ----------------       /                                                           /                                                   9*3 /   ------- + ----------------                                         |
  |    \/                                                      \/      432           144            \/                                                          \/                                                      \/      432           144                                                | |      \/                                                      \/      432           144            \/                                                          \/                                                      \/      432           144                                                | |      \/                                                          \/                                                      \/      432           144                                                   \/                                                      \/      432           144         | |      \/                                                      \/      432           144            \/                                                          \/                                                      \/      432           144                                                |
1*|x + ------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - ------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------|*|x + - ------------------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
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$$1 \left(x + \left(\frac{\sqrt{\frac{184}{3} - 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}} - \frac{2}{\sqrt{\frac{92}{3} + \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}} + 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}} - \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}}}{2} + \frac{\sqrt{\frac{92}{3} + \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}} + 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{\frac{184}{3} - 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}} + \frac{2}{\sqrt{\frac{92}{3} + \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}} + 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}} - \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}}}{2} - \frac{\sqrt{\frac{92}{3} + \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}} + 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}}{2}\right)\right) \left(x - \left(\frac{\sqrt{\frac{184}{3} - 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}} - \frac{2}{\sqrt{\frac{92}{3} + \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}} + 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}} - \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}}}{2} - \frac{\sqrt{\frac{92}{3} + \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}} + 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}}{2}\right)\right) \left(x - \left(\frac{\sqrt{\frac{184}{3} - 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}} + \frac{2}{\sqrt{\frac{92}{3} + \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}} + 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}} - \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}}}{2} + \frac{\sqrt{\frac{92}{3} + \frac{4802}{9 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}} + 2 \sqrt[3]{\frac{1872043}{432} + \frac{\sqrt{4313836623} i}{144}}}}{2}\right)\right)$$