已知代数式(x+y-6)2+根号x2-4xy+4y2的值为0,则x-y

问题描述:

已知代数式(x+y-6)2+根号x2-4xy+4y2的值为0,则x-y
x-y= ,x2+y2=.

(x+y-6)²≥0,√(x²-4xy+4y²) ≥0,(x+y-6)²+√(x²-4xy+4y²)=0,两个非负数的和为,只能都是0.所以x+y-6 =0,x²-4xy+4y²=0,即x+y-6 =0,(x-2y)²=0,解得x=4,y=2.∴x-y=2,...