已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值
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已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值
![已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值](/uploads/image/z/17998099-43-9.jpg?t=%E5%B7%B2%E7%9F%A5%28x%2By%29%5E2%3D324%2C%28x-y%29%5E2%3D16%2C%E6%B1%82xy%E5%92%8Cx%5E2%2By%5E2%E7%9A%84%E5%80%BC)
(x+y)^2=324,==>X^2+Y^2+2XY=324 (1)
(x-y)^2=16 ==>X^2+Y^2-2XY=16 (2)
(1)+(2):2(X^2+Y^2)=340 ==>X^2+Y^2=170
(1)-(2):4XY=308 ===>XY=154
(x-y)^2=16 ==>X^2+Y^2-2XY=16 (2)
(1)+(2):2(X^2+Y^2)=340 ==>X^2+Y^2=170
(1)-(2):4XY=308 ===>XY=154
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