[Quant - Inequality] Please help understanding solution / what I did wrong

[IsabellaT]

The answer here is B, please see screenshot below.

I got “cannot be determined” because I did the following:

2sqrt(x^2 + 2xy + y^2) = 16
2sqrt(x+y)(x+y)=16 -
2(x+y) = 16
2x + 2y = 16
= x+y = 8

and if x < y, there is a possibility that x = 3 and y = 5 which means it would be = and then also x=2 and y=6, so I picked D, cannot be determined. What did I do wrong?

[Leaderboard]

@IsabellaT

2sqrt(x^2 + 2xy + y^2) = 16

You seem to have missed the exponent entirely: it should be

2^{\sqrt{x^2 + 2xy + y^2}} = 16

which means that

\sqrt{x^2 + 2xy + y^2} = 4