Question

已知x不等于,x2-x=3,y2-y=3,求x2-xy+y2的值

Answer 1

构造一个方程:M^2 - M = 3

即:M^2 - M - 3 = 0

因为x^2-x=3,y^2-y=3,且x不等于y,显然,x、y是方程M^2 - M - 3 = 0的两个不相等的根.

根据韦达定理有：

x + y = 1

xy = -3

x^2-xy+y^2 = (x + y)^2 - 3xy = 1+ 9 = 10