数学问题：x2-xy-y2=0，请详细写一下怎么解
职业培训
培训职业
2025-01-02
∵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
∵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。
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