Question

若y/x+x/y=-2,求代数式2x^2+3xy-2y^2/x^2+xy-2y^2的值

Answer 1

y/x+x/y=-2

设Y/X=A

则A+1/A=-2 ==>A^2+2A+1=0==>(A+1)^2=0 ==>A=-1

所以(2x^2+3xy-2y^2)/(x^2+xy-2y^2)=(2X-Y)(X+2Y)/((X+2Y)(X-Y))

=(2X-Y)/(X-Y)=X/(X-Y)+1=1/(1-Y/X)+1=1/(1-(-1))+1=3/2