Question

Solve for (x,y) Such that

Answer 1

\[16^{x^2 + y} + 16^{y^2 + x} = 1\]

Answer 2

are those real numbers?

Answer 3

2^4(x^2+y) + 2^4(y^2+x) = 2^-1 + 2^-1

Answer 4

i tempted to start like that... and maybe equate exponents, and getting (x,y) = (-1/2, -1/2) . plz see if any flaws in my logic... guys

Answer 5

That is ONE SOLUTION.
There may be more.
Yes, they're real.

Answer 6

@mukushla im clueless plz give hint or something :)

Answer 7

clearly x<0 and y<0 and the equation is symmetric so suppose\[y\ge x \]conclude that just y=x gives us an answer

Answer 8

Howd you make that conclusion?

Answer 9

I know I;m being pretty stupid somewhere. ;/
Still, I dont see it.