Решение уравнений/ Любые/ x^4-3*x^2+4=0

Произведение корней x^4-3*x^2+4=0

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    Решение

    Сумма и произведение корней [src]
    сумма
               /    /  ___\\              /    /  ___\\              /    /  ___\\              /    /  ___\\            /    /  ___\\              /    /  ___\\            /    /  ___\\              /    /  ___\\
           |    |\/ 7 ||              |    |\/ 7 ||              |    |\/ 7 ||              |    |\/ 7 ||            |    |\/ 7 ||              |    |\/ 7 ||            |    |\/ 7 ||              |    |\/ 7 ||
           |atan|-----||              |atan|-----||              |atan|-----||              |atan|-----||            |atan|-----||              |atan|-----||            |atan|-----||              |atan|-----||
    ___    |    \  3  /|       ___    |    \  3  /|       ___    |    \  3  /|       ___    |    \  3  /|     ___    |    \  3  /|       ___    |    \  3  /|     ___    |    \  3  /|       ___    |    \  3  /|
- \/ 2 *cos|-----------| - I*\/ 2 *sin|-----------| + - \/ 2 *cos|-----------| + I*\/ 2 *sin|-----------| + \/ 2 *cos|-----------| - I*\/ 2 *sin|-----------| + \/ 2 *cos|-----------| + I*\/ 2 *sin|-----------|
           \     2     /              \     2     /              \     2     /              \     2     /            \     2     /              \     2     /            \     2     /              \     2     /
    $$\left(\left(\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)} - \sqrt{2} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)}\right) + \left(\left(- \sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)} - \sqrt{2} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)}\right) + \left(- \sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)} + \sqrt{2} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)}\right)\right)\right) + \left(\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)} + \sqrt{2} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)}\right)$$
    =
    0
    $$0$$
    произведение
    /           /    /  ___\\              /    /  ___\\\ /           /    /  ___\\              /    /  ___\\\ /         /    /  ___\\              /    /  ___\\\ /         /    /  ___\\              /    /  ___\\\
|           |    |\/ 7 ||              |    |\/ 7 ||| |           |    |\/ 7 ||              |    |\/ 7 ||| |         |    |\/ 7 ||              |    |\/ 7 ||| |         |    |\/ 7 ||              |    |\/ 7 |||
|           |atan|-----||              |atan|-----||| |           |atan|-----||              |atan|-----||| |         |atan|-----||              |atan|-----||| |         |atan|-----||              |atan|-----|||
|    ___    |    \  3  /|       ___    |    \  3  /|| |    ___    |    \  3  /|       ___    |    \  3  /|| |  ___    |    \  3  /|       ___    |    \  3  /|| |  ___    |    \  3  /|       ___    |    \  3  /||
|- \/ 2 *cos|-----------| - I*\/ 2 *sin|-----------||*|- \/ 2 *cos|-----------| + I*\/ 2 *sin|-----------||*|\/ 2 *cos|-----------| - I*\/ 2 *sin|-----------||*|\/ 2 *cos|-----------| + I*\/ 2 *sin|-----------||
\           \     2     /              \     2     // \           \     2     /              \     2     // \         \     2     /              \     2     // \         \     2     /              \     2     //
    $$\left(- \sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)} - \sqrt{2} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)}\right) \left(- \sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)} + \sqrt{2} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)}\right) \left(\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)} - \sqrt{2} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)}\right) \left(\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)} + \sqrt{2} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}{2} \right)}\right)$$
    =
                           /  ___\
                       |\/ 7 |
  /        ___\  I*atan|-----|
  |3   I*\/ 7 |        \  3  /
4*|- - -------|*e             
  \4      4   /
    $$4 \left(\frac{3}{4} - \frac{\sqrt{7} i}{4}\right) e^{i \operatorname{atan}{\left(\frac{\sqrt{7}}{3} \right)}}$$