数学问题：x2-xy-y2=0,请详细写一下怎么解
更新时间：2026-09-30 18:29:55
问题描述:
数学问题：x2-xy-y2=0,请详细写一下怎么解
刘金贵回答:
∵x²-xy-y² =(x²-xy+y²/4)-y²/4-y² =(x-y/2)²-5y²/4 =(x-y/2)²-(√5y/2)² =(x-y/2+√5y/2)(x-y/2-√5y/2) =[x-(1-√5)y/2][x-(1+√5)y/2] x²-xy-y²=0 ∴[x-(1-√5)y/2][x-(1+√5)y/2]=0 ∴x=(1±√5)y/2 反思：注意利用配方法因式分解的思路.