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-

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-
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-

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-
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

1/x³+1/y³
=(x³+y³)/(xy)³
=(x+y)(x²-xy+y²)/27
=5/27 *[(x+y)^2-3xy]
=5/27 *(25-9)
=80/27