已知x⼀y =2,求(x^2-xy+3y^2)⼀(x^2+xy+6y^2) 的值.

2025-03-06 02:37:21
推荐回答(4个)
回答1:

原式=((x/y)^2-x/y+3)/((x/y)^2+x/y+6)
代入x/y=2
=(2^2-2+3)/(2^2+2+6)
=(4-2+3)/(4+2+6)
=5/12

其实只要将(x^2-xy+3y^2) /(x^2+xy+6y^2)分子分母同除以y^2 就解了

回答2:

x/y=2
x=2y

(x^2-xy+3y^2)/(x^2+xy+6y^2)
=(4y^2-2y^2+3y^2)/(4y^2+2y^2+6y^2)
=5y^2/12y^2
=5/12

回答3:

x/y=2
则y/x=1/2
(x^2-xy+3y^2)/(x^2+xy+6y^2)
=(x/y-1+3y/x)/(x/y+1+6y/x)
=(2-1+3/2)/(2+1+3)
=5/12

回答4:

x/y =2,--->x=2y

(x^2-xy+3y^2)/(x^2+xy+6y^2)

=(4y^2-2y^2+3y^2)/(4y^2+2y^2+6y^2)

=5/12