已知X^2+Y^2=9,xy=4,则X+Y/(x^3+y^3+x+y)=?

Question

已知X^2+Y^2=9,xy=4,则X+Y/(x^3+y^3+x+y)=?

Answer 1

已知X²+Y²=9,xy=4,则(X+Y)/(x³+y³+x+y)=?
(x+y)/(x³+y³+x+y)=(x+y)[(x+y)(x²-xy+y²)+(x+y)]=1/(x²-xy+y²+1]=1/(9-4+1)=1/6