如果x/2=y/3,那么7x^2-y^2/(x^2-2xy+3y^2)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/29 21:54:01
如果x/2=y/3,那么7x^2-y^2/(x^2-2xy+3y^2)=?
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如果x/2=y/3,那么7x^2-y^2/(x^2-2xy+3y^2)=?
如果x/2=y/3,那么7x^2-y^2/(x^2-2xy+3y^2)=?

如果x/2=y/3,那么7x^2-y^2/(x^2-2xy+3y^2)=?
x/2=y/3=k
x=2k,y=3k
(7x^2-y^2)/(x^2-2xy+3y^2)
=(7*4k^2-9k^2)/(4k^2-2*6k^2+3*9k^2)
=19k^2/19k^2
=1

x=2y/3
7x^2-y^2/(x^2-2xy+3y^2)=
28/9y^2-y^2/(4/9y^2-4/3y^2+3y^2)=28/9y^2-9/19

=1

因为x/2=y/3
所以y=3x/2
代入式子得7x^2-(3x/2)^2(x^2-2x*3x/2+3*9x^2/4)
=7x^2-171x^4/16

因为x/2=y/3,所以设A=x/y=2/3
把原式7x^2-y^2/(x^2-2xy+3y^2)上下同时除以y^2
得:7A^2-1/(A^2-2A+3)=19/19=1