已知(x+y)^2=18,(x-y)^2=6求x^2+y^2和xy的值拜求!

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已知(x+y)^2=18,(x-y)^2=6求x^2+y^2和xy的值拜求!
已知(x+y)^2=18,(x-y)^2=6求x^2+y^2和xy的值
拜求!

已知(x+y)^2=18,(x-y)^2=6求x^2+y^2和xy的值拜求!
(x+y)^2=18---->(x^2+y^2)+2xy=18.(1)
,(x-y)^2=6---->(x^2+y^2)-2xy=6.(2)
(1)+(2):2(x^2+y^2)=24
x^2+y^2=12
(1)-(2):4xy=12
xy=3

x^2+y^2为两式相加除以2得12
xy为两式相减除以4得3

(x+y)^2=18 （1）
（x-y)^2=6 （2）
(1)-(2)得4xy=12,xy=3
(1)+(2)得2x^2+2y^2=24,x^2+y^2=12

展开之后相加除2是x^2+y^2的值12，相减除4是xy=3

4xy=(x+y)^2-(x-y)^2=18-6=12
xy=3
可得：x^2=4+y^2=12

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