Question

求解，已知X^2+Y^2=9,xy=4,则X+Y/(x^3+y^3+x+y)=?

各位高手，求解，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)=?
解：(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

Answer 2

原式=(x＋y)/[(x＋y)(x²－xy＋y²＋1)]
=1/[(x²＋y²)－xy＋1]
=1/6

Answer 3

1/6，由条件得出（x+y)^2=17, X+Y/(x^3+y^3+x+y)=x+y/[(x+y)^3-3xy(x+y)+x+y]=1/[(x+y)^2-3xy+1]

Answer 4

1/6，楼上正解