Question

若两个正实数x,y满足x方+2xy-3y方=0,求x方+xy+y方除以x方-xy+y方的值

Answer 1

x²+2xy-3y²=0

(x+3y)(x-y)=0

解得x=y或x=-3y

又x,y为正数

所以y=x ；x=-3y舍

(x²+xy+y²)/(x²-xy+y²)

=(x²+x²+x²)/(x²-x²+x²)

=3x²/x²

=3