求值:已知(x+y)^2=324,(x-y)^2=16,求xy及x^2+y^2的值

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求值:已知(x+y)^2=324,(x-y)^2=16,求xy及x^2+y^2的值
求值:已知(x+y)^2=324,(x-y)^2=16,求xy及x^2+y^2的值

求值:已知(x+y)^2=324,(x-y)^2=16,求xy及x^2+y^2的值
(x+y)^2=324,
x^2+y^2+2xy=324.[1]
(x-y)^2=16
x^2+y^2-2xy=16.[2]
[1]-[2]:
4xy=308
xy=77
[1]+[2]:
2(x^2+y^2)=340
x^2+y^2=170

(x+y)^2-(x-y)^2
=[(x+y)+(x-y)][(x+y)-(x-y)]
=2x*2y
=4xy=324-16=308
所以xy=77
(x+y)^2=x^2+y^2+2xy==324
x^2+y^2=324-2xy=324-77*2=170

xy=77
x^2+y^2=170