Question

Question #3dd82

Answer 1

`x^2+4y^2-4x+4y+5=0`

`rArr x^2-4x+4+4y^2+4y+1=0`

`rArr (x-2)^2+(2y+1)^2=0`

`rArr (x-2)^2=0 and (2y+1)^2 =0`

`rArr x = 2 and y = -1/2`

Putting these values after solving following equations :-

Given `(x^4-y^4)/(2x^2+xy-y^2). (2x-y)/(xy-y^2) -:(x^2+y^2/y)^2`

`rArr {(x^2)^2 - (y^2)^2}/(2x^2+2xy-xy-y^2). (2x-y)/{y(x-y)} -: (x^2+y)^2`

`rArr [(x^2+y^2)(x^2-y^2)]/[2x(x+y)-y(x+y)].(2x-y)/{y(x-y)}. 1/(x^2+y)^2`

`rArr [(x^2+y^2)(x+y)(x-y)]/[(2x-y)(x+y)]. (2x-y)/{y(x-y)}. 1/(x^2+y)^2`

`rArr (x^2+y^2)/[y(x^2+y)^2]`

`rArr [2^2+(-1/2)^2]/[(-1/2)[2^2+(-1/2)]^2]`

`rArr (4+1/4)/[(-1/2){4-1/2}^2]`

`rArr (17/4)/[(-1/2)(7/2)^2]`

`rArr -17/4. 2/1. 4/49`

`rArr - 34/49`