已知x/y=1/2,求(x²-2xy+3y²)/(x²+3xy+2y²)的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 19:30:47
已知x/y=1/2,求(x²-2xy+3y²)/(x²+3xy+2y²)的值已知x/y=1/2,求(x²-2xy+3y²)/(x²

已知x/y=1/2,求(x²-2xy+3y²)/(x²+3xy+2y²)的值
已知x/y=1/2,求(x²-2xy+3y²)/(x²+3xy+2y²)的值

已知x/y=1/2,求(x²-2xy+3y²)/(x²+3xy+2y²)的值
解: (x²-2xy+3y²)/(x²+3xy+2y²) 分子分母同时除以y²得
=[(x/y)²-2x/y+3]/[(x/y)²+3x/y+2]
=[(1/2)²-2*1/2+3]/[(1/2)²+3*1/2+2]
=(1/4-1+3)/(1/4+3/2+2)
=9/4÷15/4
=9/15
=3/5
祝你学习进步,如有不明可以追问.同意我的答案请采纳,O(∩_∩)O谢谢

x/y=1/2
y=2x
(x²-2xy+3y²)/(x²+3xy+2y²)
=(x^2-4x^2+12x^2)/(x^2+6x^2+8x^2)
=9x^2/15x^2
=3/5

x/y=1/2
设x=k y=2k
(x^2-2xy+3y^2)/(x^2+3xy+2y^2)
=(k^2-4k^2+12k^2)/(k^2+6k^2+8k^2)
=(1-4+12)/(1+6+8)
=9/15
=3/5