- #1

cng99

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## Homework Statement

This question was asked in the Indian National Maths Olympiad.

The question is:

Find all the possible real ordered pairs of (x,y) for equation

16^[(x^2) + y] + 16^[x + (y^2)]=1

## Homework Equations

That was the only equation.

## The Attempt at a Solution

Using 0.5 + 0.5 =1, (x^2) + y = -0.25 and (y^2) + x= -0.25

(Because [16^(-0.25)]=0.5 , I'm using decimals here instead of fractions)

Solving them gives one real ordered pair of (-0.5,-0.5). But how do I know if that's the only answer?