已知实数x,y满足(x+y)²=1,(x-y)²=25,求x²+y²+xy的值
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已知实数x,y满足(x+y)²=1,(x-y)²=25,求x²+y²+xy的值 用三种方法
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![已知实数x,y满足(x+y)²=1,(x-y)²=25,求x²+y²+xy的值](/uploads/image/z/18432248-32-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3%28x%2By%EF%BC%89%26%23178%3B%3D1%2C%28x-y%29%26%23178%3B%3D25%2C%E6%B1%82x%26%23178%3B%2By%26%23178%3B%2Bxy%E7%9A%84%E5%80%BC)
由(x+y)²=1,(x-y)²=25
可得:x^2+y^2=13,xy=-6
1、x²+y²+xy=13-6=7
2、x²+y²+xy=(x+y)^2-xy=1-(-6)=7
3、x²+y²+xy=(x-y)^2+3xy=25+3*(-6)=7
可得:x^2+y^2=13,xy=-6
1、x²+y²+xy=13-6=7
2、x²+y²+xy=(x+y)^2-xy=1-(-6)=7
3、x²+y²+xy=(x-y)^2+3xy=25+3*(-6)=7
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