（x-y/3)^2-(x+y/3)^2 因式分解

来源：学生作业帮编辑：搜搜考试网作业帮分类：数学作业时间：2024/06/06 02:57:58

（x-y/3)^2-(x+y/3)^2 因式分解
计算：已知（x+y)^2=18,(x-y)^2=6,求x^2+y^2及xy的值

(x-y/3)²-(x+y/3)²=(x-y/3-x-y/3)(x-y/3+x+y/3)=-2y/3*2x=-4xy/3
(x+y)²=18====>x²+y²+2xy=18(1)
(x-y)²=6=====>x²+y²-2xy=6(2)
(1)+(2)
2(x²+y²)=24
x²+y²=12
(1)-(2)
4xy=12
xy=3

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