-12*x+2*x^3-3*x^2+5=0 (уравнение)

Найду корень уравнения: -12*x+2*x^3-3*x^2+5=0

Вы ввели

           3      2        
-12*x + 2*x  - 3*x  + 5 = 0

$$- 3 x^{2} + 2 x^{3} - 12 x + 5 = 0$$

Быстрый ответ

                                    /                 1                  \     /                             /                 1                  \                             \                             
                                9*re|------------------------------------|     |                         9*im|------------------------------------|                             |                             
                                    |                     _______________|     |                             |                     _______________|                             |                             
              /    /    ___\\       |/          ___\     /           ___ |     |       /    /    ___\\       |/          ___\     /           ___ |              /    /    ___\\|              /    /    ___\\
              |atan\4*\/ 5 /|       ||  1   I*\/ 3 |    /  3   3*I*\/ 5  |     |       |atan\4*\/ 5 /|       ||  1   I*\/ 3 |    /  3   3*I*\/ 5  |       ___    |atan\4*\/ 5 /||       ___    |atan\4*\/ 5 /|
         3*cos|-------------|       ||- - - -------|*3 /   - + --------- |     |  3*sin|-------------|       ||- - - -------|*3 /   - + --------- |   3*\/ 3 *cos|-------------||   3*\/ 3 *sin|-------------|
     1        \      3      /       \\  2      2   / \/    8       2     /     |       \      3      /       \\  2      2   / \/    8       2     /              \      3      /|              \      3      /
x1 = - - -------------------- + ------------------------------------------ + I*|- -------------------- + ------------------------------------------ - --------------------------| + --------------------------
     2            4                                 4                          \           4                                 4                                    4             /               4             

$$x_{1} = - \frac{3}{4} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (4 \sqrt{5} \right )} \right )} + \frac{9}{4} \Re{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{8} + \frac{3 i}{2} \sqrt{5}}}\right)} + \frac{1}{2} + \frac{3 \sqrt{3}}{4} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (4 \sqrt{5} \right )} \right )} + i \left(- \frac{3 \sqrt{3}}{4} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (4 \sqrt{5} \right )} \right )} - \frac{3}{4} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (4 \sqrt{5} \right )} \right )} + \frac{9}{4} \Im{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{8} + \frac{3 i}{2} \sqrt{5}}}\right)}\right)$$

                                    /                 1                  \     /                             /                 1                  \                             \                             
                                9*re|------------------------------------|     |                         9*im|------------------------------------|                             |                             
                                    |                     _______________|     |                             |                     _______________|                             |                             
              /    /    ___\\       |/          ___\     /           ___ |     |       /    /    ___\\       |/          ___\     /           ___ |              /    /    ___\\|              /    /    ___\\
              |atan\4*\/ 5 /|       ||  1   I*\/ 3 |    /  3   3*I*\/ 5  |     |       |atan\4*\/ 5 /|       ||  1   I*\/ 3 |    /  3   3*I*\/ 5  |       ___    |atan\4*\/ 5 /||       ___    |atan\4*\/ 5 /|
         3*cos|-------------|       ||- - + -------|*3 /   - + --------- |     |  3*sin|-------------|       ||- - + -------|*3 /   - + --------- |   3*\/ 3 *cos|-------------||   3*\/ 3 *sin|-------------|
     1        \      3      /       \\  2      2   / \/    8       2     /     |       \      3      /       \\  2      2   / \/    8       2     /              \      3      /|              \      3      /
x2 = - - -------------------- + ------------------------------------------ + I*|- -------------------- + ------------------------------------------ + --------------------------| - --------------------------
     2            4                                 4                          \           4                                 4                                    4             /               4             

$$x_{2} = \frac{9}{4} \Re{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{8} + \frac{3 i}{2} \sqrt{5}}}\right)} - \frac{3}{4} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (4 \sqrt{5} \right )} \right )} - \frac{3 \sqrt{3}}{4} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (4 \sqrt{5} \right )} \right )} + \frac{1}{2} + i \left(\frac{9}{4} \Im{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{8} + \frac{3 i}{2} \sqrt{5}}}\right)} - \frac{3}{4} \sin{\left (\frac{1}{3} \operatorname{atan}{\left (4 \sqrt{5} \right )} \right )} + \frac{3 \sqrt{3}}{4} \cos{\left (\frac{1}{3} \operatorname{atan}{\left (4 \sqrt{5} \right )} \right )}\right)$$

              _______________                         
             /           ___                          
     1      /  3   3*I*\/ 5               9           
x3 = - + 3 /   - + ---------  + ----------------------
     2   \/    8       2               _______________
                                      /           ___ 
                                     /  3   3*I*\/ 5  
                                4*3 /   - + --------- 
                                  \/    8       2     

$$x_{3} = \frac{1}{2} + \frac{9}{4 \sqrt[3]{\frac{3}{8} + \frac{3 i}{2} \sqrt{5}}} + \sqrt[3]{\frac{3}{8} + \frac{3 i}{2} \sqrt{5}}$$

Численный ответ

x1 = 0.388684544541000

x2 = -2.04062936195000

x3 = 3.15194481741000

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