Question

Пусть x1 и x2 корни уравнения 2x^2-5x-4=0.....

Answer 1

2x²-5x-4=0
1
x1+x2=-5/2 U x1*x2=-2
1/x1²+1/x2²=(x1²+x2²)/(x1x2)²=[(x1+x2)²-2x1x2]/(x1x2)²=(6,25+4)/4=10,25/4=
=2,2625
2
x1x2^4+x2x1^4=x1x2(x1³+x2³)=x1x2(x1+x2)(x1²-x1x2+x2²)=
=x1x2(x1+x2)[(x1+x2)²-3x1x2]=-2*2,5*(6,25+6)=-5*12,25=-61,25