已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求式子xy(x²+y²)
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![已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求式子xy(x²+y²)](/uploads/image/z/1343990-38-0.jpg?t=%E5%B7%B2%E7%9F%A5x%E3%80%81y%E7%9A%84%E6%96%B9%E7%A8%8B%E7%BB%843%EF%BC%88x%26%23178%3B%2By%26%23178%3B%EF%BC%89-5xy%3D6%2C2%EF%BC%88x%26%23178%3B%2By%26%23178%3B%EF%BC%89%2Bxy%3D17%2C%E6%B1%82%E5%BC%8F%E5%AD%90xy%EF%BC%88x%26%23178%3B%2By%26%23178%3B%EF%BC%89)
已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求式子xy(x²+y²)
已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求式子xy(x²+y²)
已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求式子xy(x²+y²)
3(x²+y²)-5xy=6 (1)
2(x²+y²)+xy=17 (2)
2*(1)-3*(2)
-10xy-3xy=12-3*17
xy=3
带入(1)
x²+y²=7
xy(x²+y²)=3*7=21
3(x²+y²)-5xy=6,(1)
2(x²+y²)+xy=17 (2)
(1)×2-(2)×3得xy=3
代入(1)得x²+y²=7
∴xy(x²+y²) =3×7=21