Question

已知x²-3xy-4y²=0(y≠0),求代数式x-y分之x+2y的值

已知x²-3xy-4y²=0(y≠0),求代数式x-y分之x+2y的值
详细步骤 谢谢了

Answer 1

x^2-3xy-4y^2=0
(x-4y)(x+y)=0
x=4y或x=-y

当x=4y时
(x+2y)/(x-y)
=(4y+2y)/(4y-y)
=6y/3y
=2

当x=-y时
(x+2y)/(x-y)
=(-y+2y)/(-y-y)
=y/(-2y)
=-1/2

Answer 2

x²-3xy-4y²=0
（x-4y)(x+y)=0
∴x=4y或x=-y
当x=4y时（x+2y）/(x-y)=6y/3y=2
当x=-y时（x+2y）/(x-y)=y/(-2y)=-1/2

Answer 3

由x²-3xy-4y²=0得（x+y)(x-4y)=0
所以x=-y或x=4y
当x=-y时
（x+2y）/(x-y)=-1/2
当x=4y时
(x+2y）/(x-y)=2