已知(x+y)²=18,(x-y)²=6,求x²+y²及xy的值
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![已知(x+y)²=18,(x-y)²=6,求x²+y²及xy的值](/uploads/image/z/813030-6-0.jpg?t=%E5%B7%B2%E7%9F%A5%28x%2By%29%26%23178%3B%3D18%2C%28x-y%29%26%23178%3B%3D6%2C%E6%B1%82x%26%23178%3B%2By%26%23178%3B%E5%8F%8Axy%E7%9A%84%E5%80%BC)
已知(x+y)²=18,(x-y)²=6,求x²+y²及xy的值
已知(x+y)²=18,(x-y)²=6,求x²+y²及xy的值
已知(x+y)²=18,(x-y)²=6,求x²+y²及xy的值
由(x+y)²=18得
x^2+2xy+y^2=18 (1)
由,(x-y)²=6得
X^2-2XY+Y^2=6 (2)
(1)+(2)得出 2(x²+y²)=24 即x²+y²=12
(1)-(2)得出 4XY=12 即XY=3