Question

若x+y=2,且（x+2）（y+2）=5,求x^2+xy+y^2的值

Answer 1

因为 (x+2)(y+2) = xy+2(x+y)+4 = 5,而 x+y=2,所以 xy=-3.

因此 x^2+xy+y^2 = (x+y)^2-xy = 2^2-(-3) = 7.

即 x^2+xy+y^2 = 7.