已知x+y=5,xy=3,x³+y³=(x+y)(x²-xy+y²),则1/x&
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已知x+y=5,xy=3,x³+y³=(x+y)(x²-xy+y²),则1/x³+1/y³=?
到底谁是对的-
到底谁是对的-
![已知x+y=5,xy=3,x³+y³=(x+y)(x²-xy+y²),则1/x&](/uploads/image/z/8030552-32-2.jpg?t=%E5%B7%B2%E7%9F%A5x%2By%3D5%2Cxy%3D3%2Cx%26%23179%3B%2By%26%23179%3B%3D%28x%2By%29%28x%26%23178%3B-xy%2By%26%23178%3B%29%2C%E5%88%991%2Fx%26)
已知x+y=5,xy=3,x³+y³=(x+y)(x²-xy+y²),则1/x³+1/y³=?
解,得:
因为x+y=5
所以(x+y)^2==25
x^2+2xy+y^2==25
所以
x^2-xy+y^2+3xy==25
x^2-xy+y^2==25-3xy
x^2-xy+y^2==25-9
x^2-xy+y^2==6
所以
x³+y³=(x+y)(x²-xy+y²)
=5*6
=30
因为:
1/x³+1/y³
==(y^3+x^3)/x^3y^3
==30/27
==10/9
==1又1/9
解,得:
因为x+y=5
所以(x+y)^2==25
x^2+2xy+y^2==25
所以
x^2-xy+y^2+3xy==25
x^2-xy+y^2==25-3xy
x^2-xy+y^2==25-9
x^2-xy+y^2==6
所以
x³+y³=(x+y)(x²-xy+y²)
=5*6
=30
因为:
1/x³+1/y³
==(y^3+x^3)/x^3y^3
==30/27
==10/9
==1又1/9
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