1,因为x1,x2为方程的实根,由韦达定理可以知道:
x1+x2= -(k-5)
x1*x2= -(k+4)
(x1+1)*(x2+1)=-8
解三元一次方程组可得:
k=5
x1=3
x2=-3
所以,K值为5,两根为3,-3.
2,因为x1,x2为方程2x^2+4x-3=0的两个实数根,由韦达定理知:
x1+x2=-2
x1*x2=-3/2
所以:
(1)x1^2*x2+x1*x2^2
=x1*x2(x1+x2)
=3
(2)-1/x1-1/x2
=-(x2+x1)/(x1x2)
=-4/3
(3)x1^2+x2^2
=(x1+x2)^2-2x1x2
=4+3
=7
(4)x1^2+x1x2+x2^2
=(x1+x2)^2-x1x2
=4+3/2
=5.5
(5)(x1-2)(x2-2)
=x1x2-2(x1+x2)+4
=-1.5+4+4
=6.5