Question

2乘X平方+3XY减2乘Y平方=0,XY不等于0,求X平方减Y平方分之3乘X平方+4XY加5乘Y平方的值

Answer 1

2x^2+3xy-2y^2=0

(2x-y)(x+2y)=0

y=2x或x=-2y

当y=2x时

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

=[3x^2+4x*2x+5*(2x)^2]/[x^2-(2x)^2]

=[3x^2+8x^2+20x^2]/[x^2-4x^2]

=(31x^2)/(-3x^2)

=-31/3

当x=-2y时

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

=[3*(-2y)^2+4*(-2y)*y+5*y^2]/[(-2y)^2-y^2]

=[12y^2-8y^2+5y^2]/[4y^2-y^2]

=(9y^2)/(3y^2)

=3