4*x^3-48*x+3=0 (уравнение)

Уравнение с неизвестным  :

Искать численное решение на промежутке [, ]

    Найду корень уравнения: 4*x^3-48*x+3=0

    Решение

    Вы ввели
    [LaTeX]
       3               
    4*x  - 48*x + 3 = 0
    $$4 x^{3} - 48 x + 3 = 0$$
    График
    [LaTeX]
    Быстрый ответ
    [LaTeX]
                                                                /                                                              /    /  ______\\      /    /  ______\\\            /    /  ______\\      /    /  ______\\
                                                                |                                                              |    |\/ 4087 ||      |    |\/ 4087 |||            |    |\/ 4087 ||      |    |\/ 4087 ||
                                                                |                                                              |atan|--------||      |atan|--------|||            |atan|--------||      |atan|--------||
                /                    1                    \     |       /                    1                    \     ___    |    \   3    /|      |    \   3    /||     ___    |    \   3    /|      |    \   3    /|
    x1 = - 12*re|-----------------------------------------| + I*|- 12*im|-----------------------------------------| + \/ 3 *cos|--------------| + sin|--------------|| - \/ 3 *sin|--------------| + cos|--------------|
                |                     ____________________|     |       |                     ____________________|            \      3       /      \      3       /|            \      3       /      \      3       /
                |/          ___\     /             ______ |     |       |/          ___\     /             ______ |                                                  |                                                  
                ||  1   I*\/ 3 |    /  81   27*I*\/ 4087  |     |       ||  1   I*\/ 3 |    /  81   27*I*\/ 4087  |                                                  |                                                  
                ||- - - -------|*3 /   -- + ------------- |     |       ||- - - -------|*3 /   -- + ------------- |                                                  |                                                  
                \\  2      2   / \/    8          8       /     \       \\  2      2   / \/    8          8       /                                                  /                                                  
    $$x_{1} = - \sqrt{3} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{4087}}{3} \right )} \right )} - 12 \Re{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{81}{8} + \frac{27 i}{8} \sqrt{4087}}}\right)} + \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{4087}}{3} \right )} \right )} + i \left(- 12 \Im{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{81}{8} + \frac{27 i}{8} \sqrt{4087}}}\right)} + \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{4087}}{3} \right )} \right )} + \sqrt{3} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{4087}}{3} \right )} \right )}\right)$$
                                                                /                                                              /    /  ______\\      /    /  ______\\\            /    /  ______\\      /    /  ______\\
                                                                |                                                              |    |\/ 4087 ||      |    |\/ 4087 |||            |    |\/ 4087 ||      |    |\/ 4087 ||
                                                                |                                                              |atan|--------||      |atan|--------|||            |atan|--------||      |atan|--------||
                /                    1                    \     |       /                    1                    \     ___    |    \   3    /|      |    \   3    /||     ___    |    \   3    /|      |    \   3    /|
    x2 = - 12*re|-----------------------------------------| + I*|- 12*im|-----------------------------------------| - \/ 3 *cos|--------------| + sin|--------------|| + \/ 3 *sin|--------------| + cos|--------------|
                |                     ____________________|     |       |                     ____________________|            \      3       /      \      3       /|            \      3       /      \      3       /
                |/          ___\     /             ______ |     |       |/          ___\     /             ______ |                                                  |                                                  
                ||  1   I*\/ 3 |    /  81   27*I*\/ 4087  |     |       ||  1   I*\/ 3 |    /  81   27*I*\/ 4087  |                                                  |                                                  
                ||- - + -------|*3 /   -- + ------------- |     |       ||- - + -------|*3 /   -- + ------------- |                                                  |                                                  
                \\  2      2   / \/    8          8       /     \       \\  2      2   / \/    8          8       /                                                  /                                                  
    $$x_{2} = \sqrt{3} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{4087}}{3} \right )} \right )} + \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{4087}}{3} \right )} \right )} - 12 \Re{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{81}{8} + \frac{27 i}{8} \sqrt{4087}}}\right)} + i \left(- \sqrt{3} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{4087}}{3} \right )} \right )} + \sin{\left (\frac{1}{3} \operatorname{atan}{\left (\frac{\sqrt{4087}}{3} \right )} \right )} - 12 \Im{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{81}{8} + \frac{27 i}{8} \sqrt{4087}}}\right)}\right)$$
                                            ____________________
                                           /             ______ 
                                          /  81   27*I*\/ 4087  
                                       3 /   -- + ------------- 
                       12              \/    8          8       
    x3 = - ------------------------- - -------------------------
                ____________________               3            
               /             ______                             
              /  81   27*I*\/ 4087                              
           3 /   -- + -------------                             
           \/    8          8                                   
    $$x_{3} = - \frac{1}{3} \sqrt[3]{\frac{81}{8} + \frac{27 i}{8} \sqrt{4087}} - \frac{12}{\sqrt[3]{\frac{81}{8} + \frac{27 i}{8} \sqrt{4087}}}$$
    Численный ответ
    [LaTeX]
    x1 = 3.43241826724000
    x2 = 0.0625203649462000
    x3 = -3.49493863218000