Решение уравнений/ Любые/ x^2=c

Сумма корней x^2=c

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    Решение

    Сумма и произведение корней [src]
    сумма
         _________________                                 _________________                               _________________                                 _________________                         
  4 /   2        2        /atan2(im(c), re(c))\     4 /   2        2        /atan2(im(c), re(c))\   4 /   2        2        /atan2(im(c), re(c))\     4 /   2        2        /atan2(im(c), re(c))\
- \/  im (c) + re (c) *cos|-------------------| - I*\/  im (c) + re (c) *sin|-------------------| + \/  im (c) + re (c) *cos|-------------------| + I*\/  im (c) + re (c) *sin|-------------------|
                          \         2         /                             \         2         /                           \         2         /                             \         2         /
    (−i(re⁡(c))2+(im⁡(c))24sin⁡(atan2⁡(im⁡(c),re⁡(c))2)−(re⁡(c))2+(im⁡(c))24cos⁡(atan2⁡(im⁡(c),re⁡(c))2))+(i(re⁡(c))2+(im⁡(c))24sin⁡(atan2⁡(im⁡(c),re⁡(c))2)+(re⁡(c))2+(im⁡(c))24cos⁡(atan2⁡(im⁡(c),re⁡(c))2))\left(- i \sqrt[4]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{2} \right)}\right)
    =
    0
    00
    произведение
    /     _________________                                 _________________                         \ /   _________________                                 _________________                         \
|  4 /   2        2        /atan2(im(c), re(c))\     4 /   2        2        /atan2(im(c), re(c))\| |4 /   2        2        /atan2(im(c), re(c))\     4 /   2        2        /atan2(im(c), re(c))\|
|- \/  im (c) + re (c) *cos|-------------------| - I*\/  im (c) + re (c) *sin|-------------------||*|\/  im (c) + re (c) *cos|-------------------| + I*\/  im (c) + re (c) *sin|-------------------||
\                          \         2         /                             \         2         // \                        \         2         /                             \         2         //
    (−i(re⁡(c))2+(im⁡(c))24sin⁡(atan2⁡(im⁡(c),re⁡(c))2)−(re⁡(c))2+(im⁡(c))24cos⁡(atan2⁡(im⁡(c),re⁡(c))2))(i(re⁡(c))2+(im⁡(c))24sin⁡(atan2⁡(im⁡(c),re⁡(c))2)+(re⁡(c))2+(im⁡(c))24cos⁡(atan2⁡(im⁡(c),re⁡(c))2))\left(- i \sqrt[4]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{2} \right)}\right)
    =
        _________________                       
   /   2        2      I*atan2(im(c), re(c))
-\/  im (c) + re (c) *e
    −(re⁡(c))2+(im⁡(c))2eiatan2⁡(im⁡(c),re⁡(c))- \sqrt{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}
    Теорема Виета
    это приведённое квадратное уравнение
    px+q+x2=0p x + q + x^{2} = 0
    где
    p=bap = \frac{b}{a}
    p=0p = 0
    q=caq = \frac{c}{a}
    q=−cq = - c
    Формулы Виета
    x1+x2=−px_{1} + x_{2} = - p
    x1x2=qx_{1} x_{2} = q
    x1+x2=0x_{1} + x_{2} = 0
    x1x2=−cx_{1} x_{2} = - c