（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

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（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
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（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 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 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

(x+y)^2=x^2+y^2+2xy (x-y)^2=x^2+y^2-2xy两式想加，除以2得x^2+y^2两式相减除以四得xy

如图

=665884

1)原式=(x-y/3+x+y/3)(x-y/3-x-y/3)
=2x*(-2y/3)
=-4/3xy
2)x^2+y^2+2xy=18 x^2+y^2-2xy=6
2*(x^2+y^2)=24
x^2+y^2=12
2xy=6
xy=3

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