GMAT TIGER wrote:

spriya wrote:

if x+y^2 = (x+y^2)^2 whats is the value of y?

1)x=y^2

2)xy^2=0

HELP NEEDED ,i got confused between equations

x+y^2 = (x+y^2)^2

x+y^2 = x^2+2xy^2+y^4

from1: x = y^2

x+y^2 = x^2+2xy^2+y^4

y^2+y^2 = y^4+2y^2y^2+y^4

2y^2 = 4y^4

y^2 = 2y^4........A

2y^4 - y^2 = 0

y^2 (2y^2 - 1) = 0

y = 0 or 1/2.........B

nsf...

from 2: xy^2 = 0

either x or y or both = 0

x+y^2 = x^2+2xy^2+y^4

x+y^2 = x^2+y^4

if x = 0:

y^2 = y^4

y^4 - y^2 = 0

y2 (y^2 -1) = 0

y = -1, 0, 1

so nsf..

from 1 and 2: y = 0

C.

if we substitute B in A, it does not satisfy the eqn, so how 1/2 is a soln?

am i missing something?