2x²-5x-4=0,x1+x2=5/2=2,5; x1x2= -2 по т.Виета.
1)1/x1²+1/x2²= (x1²+x2²)/(x1·x2)²=( (x1+x2)²-2x1x2) /(x1x2)²=(2,5²+4) /(-2)²=10,25/4=
2,5625=2 9/16.
2)x1x2^4+x2x1^4=x1·x2(x2³+x1³)=x1·x2·(x1+x2)(x1²-x1·x2+x2²)=
x1·x2(x1+x2)((x1+x2)²-3x1·x2)= -2·2,5(2,5²-3(-2))= -5(6,25+6)=-5·12,25=-61,25.