Произведение корней x^2+sqrt(-a+x)*(x-1)=x

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    Решение

    Сумма и произведение корней [src]
    сумма
               ____________________________                                          ____________________________                                            ____________________________                                          ____________________________                                  
            4 /              2        2        /atan2(-4*im(a), 1 - 4*re(a))\     4 /              2        2        /atan2(-4*im(a), 1 - 4*re(a))\       4 /              2        2        /atan2(-4*im(a), 1 - 4*re(a))\     4 /              2        2        /atan2(-4*im(a), 1 - 4*re(a))\
            \/  (1 - 4*re(a))  + 16*im (a) *cos|----------------------------|   I*\/  (1 - 4*re(a))  + 16*im (a) *sin|----------------------------|       \/  (1 - 4*re(a))  + 16*im (a) *cos|----------------------------|   I*\/  (1 - 4*re(a))  + 16*im (a) *sin|----------------------------|
        1                                      \             2              /                                        \             2              /   1                                      \             2              /                                        \             2              /
    1 + - - ----------------------------------------------------------------- - ------------------------------------------------------------------- + - + ----------------------------------------------------------------- + -------------------------------------------------------------------
        2                                   2                                                                    2                                    2                                   2                                                                    2                                 
    $$\left(\left(- \frac{i \sqrt[4]{\left(1 - 4 \operatorname{re}{\left(a\right)}\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 4 \operatorname{im}{\left(a\right)},1 - 4 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{\left(1 - 4 \operatorname{re}{\left(a\right)}\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 4 \operatorname{im}{\left(a\right)},1 - 4 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{2} + \frac{1}{2}\right) + 1\right) + \left(\frac{i \sqrt[4]{\left(1 - 4 \operatorname{re}{\left(a\right)}\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 4 \operatorname{im}{\left(a\right)},1 - 4 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(1 - 4 \operatorname{re}{\left(a\right)}\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 4 \operatorname{im}{\left(a\right)},1 - 4 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{2} + \frac{1}{2}\right)$$
    =
    2
    $$2$$
    произведение
    /       ____________________________                                          ____________________________                                  \ /       ____________________________                                          ____________________________                                  \
    |    4 /              2        2        /atan2(-4*im(a), 1 - 4*re(a))\     4 /              2        2        /atan2(-4*im(a), 1 - 4*re(a))\| |    4 /              2        2        /atan2(-4*im(a), 1 - 4*re(a))\     4 /              2        2        /atan2(-4*im(a), 1 - 4*re(a))\|
    |    \/  (1 - 4*re(a))  + 16*im (a) *cos|----------------------------|   I*\/  (1 - 4*re(a))  + 16*im (a) *sin|----------------------------|| |    \/  (1 - 4*re(a))  + 16*im (a) *cos|----------------------------|   I*\/  (1 - 4*re(a))  + 16*im (a) *sin|----------------------------||
    |1                                      \             2              /                                        \             2              /| |1                                      \             2              /                                        \             2              /|
    |- - ----------------------------------------------------------------- - -------------------------------------------------------------------|*|- + ----------------------------------------------------------------- + -------------------------------------------------------------------|
    \2                                   2                                                                    2                                 / \2                                   2                                                                    2                                 /
    $$\left(- \frac{i \sqrt[4]{\left(1 - 4 \operatorname{re}{\left(a\right)}\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 4 \operatorname{im}{\left(a\right)},1 - 4 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{\left(1 - 4 \operatorname{re}{\left(a\right)}\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 4 \operatorname{im}{\left(a\right)},1 - 4 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{2} + \frac{1}{2}\right) \left(\frac{i \sqrt[4]{\left(1 - 4 \operatorname{re}{\left(a\right)}\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 4 \operatorname{im}{\left(a\right)},1 - 4 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(1 - 4 \operatorname{re}{\left(a\right)}\right)^{2} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 4 \operatorname{im}{\left(a\right)},1 - 4 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{2} + \frac{1}{2}\right)$$
    =
    I*im(a) + re(a)
    $$\operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)}$$
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