Question

x1+x2=-40 x1×x2=-1600

Answer 1

Ответ:

Объяснение:

$[left{begin{gathered}{x_1}+{x_2}=-40hfill\{x_1}cdot{x_2}=-1600hfill\end{gathered}right.Leftrightarrowleft{begin{gathered}{x_1}=-40-{x_2}hfill\{x_1}cdot{x_2}=-1600hfill\end{gathered}right.Leftrightarrow]$

$[left{begin{gathered}{x_1}=-40-{x_2}hfill\(-40-{x_2})cdot{x_2}=-1600hfill\end{gathered}right.Leftrightarrowleft{begin{gathered}{x_1}=-40-{x_2}hfill\-40{x_2}-x_2^2+1600=0hfill\end{gathered}right.]$

Решим квадратное уравнение:

$[begin{gathered}-40{x_2}-x_2^2+1600=0hfill\-40x-{x^2}+1600=0;;;;|cdot (-1)hfill\{x^2}+40x-1600=0hfill\D={b^2}-4ac={40^2}+4cdot 1cdot1600=1600+6400=8000hfill\end{gathered}]$

$[begin{gathered}{x_{1;2}}=frac{{-bpmsqrt D}}{{2a}}=frac{{-40pmsqrt {8000}}}{{2cdot 1}}=frac{{-40pm40sqrt 5}}{2}hfill\{x_1}=frac{{-40+40sqrt 5}}{2}=frac{{2(-20+20sqrt 5)}}{2}=-20+20sqrt 5hfill\{x_2}=frac{{-40-40sqrt 5}}{2}=frac{{2(-20-20sqrt 5)}}{2}=-20-20sqrt 5hfill\end{gathered}]$

Итак, мы нашли x₂.

${x_2}=-20+20sqrt 5$

или

${x_2}=-20-20sqrt 5$

Найдем x₁

${x_1}=-40-{x_2}hfill$

При ${x_2}=-20+20sqrt 5$  

$[begin{gathered}{x_1}=-40-(-20+20sqrt 5)=-20-20sqrt 5hfill\end{gathered}]$

При ${x_2}=-20-20sqrt 5$

$[{x_1}=-40-(-20-20sqrt 5)=-20+20sqrt 5]$

Ответ: $[{x_1}=-20-20sqrt 5;;;;{x_2}=-20+20sqrt 5]$   или $[{x_1}=-20+20sqrt 5;{x_2}=-20-20sqrt 5]$