已知(x+y)²=49,(x+y)²=1,求x²+y²的值打错了,应该是:已知(x+y)²=49,(x-y)²=1,求x²+y²的值
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![已知(x+y)²=49,(x+y)²=1,求x²+y²的值打错了,应该是:已知(x+y)²=49,(x-y)²=1,求x²+y²的值](/uploads/image/z/3766504-40-4.jpg?t=%E5%B7%B2%E7%9F%A5%28x%2By%29%26%23178%3B%3D49%2C%28x%2By%29%26%23178%3B%3D1%2C%E6%B1%82x%26%23178%3B%2By%26%23178%3B%E7%9A%84%E5%80%BC%E6%89%93%E9%94%99%E4%BA%86%EF%BC%8C%E5%BA%94%E8%AF%A5%E6%98%AF%EF%BC%9A%E5%B7%B2%E7%9F%A5%28x%2By%29%26%23178%3B%3D49%2C%28x-y%29%26%23178%3B%3D1%2C%E6%B1%82x%26%23178%3B%2By%26%23178%3B%E7%9A%84%E5%80%BC)
已知(x+y)²=49,(x+y)²=1,求x²+y²的值打错了,应该是:已知(x+y)²=49,(x-y)²=1,求x²+y²的值
已知(x+y)²=49,(x+y)²=1,求x²+y²的值
打错了,应该是:已知(x+y)²=49,(x-y)²=1,求x²+y²的值
已知(x+y)²=49,(x+y)²=1,求x²+y²的值打错了,应该是:已知(x+y)²=49,(x-y)²=1,求x²+y²的值
解其中一个是x-y吧,不妨是(x-y)²=1
则由(x+y)²=x²+2xy+y²=49
(x-y)²=x²-2xy+y²=1
两式相加得2(x²+y²)=49+1
即x²+y²=25
题目应是 已知(x-y)²=49,(x+y)²=1,求x²+y²的值
(x-y)²=49
x²-2xy+y²=49 (1)
(x+y)²=1
x²+2xy+y²=1 (2)
(1)+(2)得
2(x²+y²)=49+1
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题目应是 已知(x-y)²=49,(x+y)²=1,求x²+y²的值
(x-y)²=49
x²-2xy+y²=49 (1)
(x+y)²=1
x²+2xy+y²=1 (2)
(1)+(2)得
2(x²+y²)=49+1
x²+y²=25
收起
因为(x+y)²=49,
所以x²+y²+2xy=49
因为(x-y)²=1,
所以x²+y²-2xy=1
所以2x²+2y²=50
x²+y²=25