Question

若x^2+xy-2y^2=0,则(x^2+3xy+y^2）/(x^2+y^2)=多少

Answer 1

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

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

x=-2y or x=y

x=-2y

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

=(4y^2-6y^2+y^2)/5y^2

=-1/5

x=y

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

=5y^2/2y^2

=5/2