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

Сумма и произведение корней

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)

$$\operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)}$$