Question

Решите, по теореме Виета :)

Answer 1

$x_1\cdot x_2=\frac{c}{a}=-\frac{4}{2}=-2;\ x_1+x_2=-\frac{b}{a}=\frac{5}{2}$

$\frac{1}{x_1^2}+\frac{1}{x_2^2}=\frac{x_2^2+x_1^2}{x_1^2x_2^2}= \frac{(x_1+x_2)^2-2x_1x_2}{(x_1x_2)^2}=\frac{(25/4)+4}{4}= \frac{41}{16};$

$x_1x_2^4+x_2x_1^4=x_1x_2(x_1^3+x_2^3)=-2(x_1+x_2)(x_1^2-x_1x_2+x_2^2)=$

$=-2\cdot \frac{5}{2}((x_1+x_2)^2-3x_1x_2)=-5(\frac{25}{4}+6)=-5\cdot \frac{49}{4}=-\frac{245}{4}$