An algebra problem by A Former Brilliant Member

Algebra Level 4

Find the number of pairs of real numbers ( x , y ) (x,y) such that

1 6 x 2 + y + 1 6 y 2 + x = 1. \large 16^{x^2 + y } + 16^{y^2 + x} = 1 .


The answer is 1.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Answer is (-0.5,-0.5). We can get 1 by adding 0.5 and 0.5. 0.5 is 1 6 − 0.25 16^{-0.25} so we need both the exponents to be -0.25.

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