Question

若x²+y²=12,xy=4,求x-y、x²-y²的值

Answer 1

因为 (x-y)^2=x^2+y^2-2xy=4

所以 x-y=2或x-y=-2

(x+y)^2=x^2+y^2+2xy=20

所以x+y=2倍根号5或-2倍根号5

所以x^2-y^2=(x+y)(x-y)=4倍根号5或-4倍根号5