Question

(2)已知 x+y=-5 xy=6 求x(x/y)+y(y/x？

Answer 1

求式子x(x/y)+y(y/x)的值
很显然x(x/y)+y(y/x)
=(x³ +y³)/xy
=(x+y)(x² -xy +y²) /xy
=(x+y)[(x+y)² -3xy]/xy
于是代入x+y= -5，xy=6
式子的值= -5 *7/6= -35/6

Answer 2

x²+y²=(x+y)²－2xy
=(-5)²－2×6=25－12=13
则x(x/y) + y(y/x)=x²/y + y²/x
=(x³ + y³)/xy
=[(x+y)(x²-xy+y²)]/xy
=[(-5)×(13－6)]/6
=-35/6