已知:x/y=4/5,求y²/(x²-xy+y²)的值

已知:x/y=4/5,求y²/(x²-xy+y²)的值
已知:x/y=4/5,求y²/(x²-xy+y²)的值

已知:x/y=4/5,求y²/(x²-xy+y²)的值
解
x/y=4/5
∴x=4/5y
∴
y²/(x²-xy+y²)
=y²/[(4/5y)²-(4/5y)y+y²]
=y²/[16/25y²-4/5y²+y²]
=y²/(-4/25y²+y²)
=y²/(21/25y²)
=25/21

答：
x/y=4/5
y²/(x²-xy+y²) 分子分母同除以y²得：
=1/[(x/y)²-(x/y)+1]
=1/[(4/5)²-4/5+1]
=1/(16/25+1/5)
=1/(21/25)
=25/21

y²/(x²-xy+y²)
=1/(x/y)²-x/y+1)
=1/（16/25-4/5+1)
=1/(21/25)
=25/21