Question

已知X1,X2是方程2x^2-3x-1=0的两个根,利用根与系数的关系,求值：x1^3x2+x1x2的三次方

Answer 1

由韦达定理有

x1+x2=3/2 x1*x2=-1/2

x1^3x2+x1x2^3

=x1x2(x1^2+x2^2)

=x1x2[(x1+x2)^2-2x1x2]

=-1/2*(9/4+1)

=-13/8