已知(x+y)^2=9,(x-y)^2=5,求x^2+y^2和xy的值
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![已知(x+y)^2=9,(x-y)^2=5,求x^2+y^2和xy的值](/uploads/image/z/5443578-18-8.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%88x%2By%EF%BC%89%5E2%3D9%2C%EF%BC%88x-y%EF%BC%89%5E2%3D5%2C%E6%B1%82x%5E2%2By%5E2%E5%92%8Cxy%E7%9A%84%E5%80%BC)
已知(x+y)^2=9,(x-y)^2=5,求x^2+y^2和xy的值
已知(x+y)^2=9,(x-y)^2=5,求x^2+y^2和xy的值
已知(x+y)^2=9,(x-y)^2=5,求x^2+y^2和xy的值
(x+y)^2+(x-y)^2=2(x^2+y^2)=9+5=14
所以x^2+y^2=7
(x+y)^2-(x-y)^2=4xy=9-5=4
所以xy=1
(x+y)^2=x^2+2xy+y^2=9.....(1)
(x-y)^2=x^2-2xy+y^2=5......(2)
(1)+(2):2(x^2+y^2)=14
x^2+y^2=7
(1)-(2):4xy=4
xy=1