已知2x=3y,求3x^2/4y^2的值已知x/3=y/4=z/5≠0,则x+y+z/x-y+z的值当x=3,y=2时,4xy-4x^2-y^2/2x-y的值已知x-y=4xy,求2x+3y-2y/x-2xy-y的值

Question

已知2x=3y,求3x^2/4y^2的值
已知x/3=y/4=z/5≠0,则x+y+z/x-y+z的值
当x=3,y=2时,4xy-4x^2-y^2/2x-y的值
已知x-y=4xy,求2x+3y-2y/x-2xy-y的值

Answer 1

2x/3y=1等式两边平方
则4x^2/9y^2=1
所以x^2/y^2=9/4
3x^2/4y^2=(9/4)×(3/4)=27/16
令x/3=y/4=z/5=m
则x=3m,y=4m,z=5m
(x+y+z)/(x-y+z)=(3m+4m+5m)/(3m-4m+5m)
=12m/4m
=3
x=3,y=2
(4xy-4x^2-y^2)/(2x-y)
=-(4x^2-4xy+y^2)/(2x-y)
=-(2x-y)^2/(2x-y)
=-(2x-y)
=y-2x
=2-2×3
=-4
x-y=4xy
(2x+3xy-2y)/(x-2xy-y)
=[2(x-y)+3xy]/[(x-y)-2xy]
=(8xy+3xy)/(4xy-2xy)
=11xy/2xy
=11/2