RMO 2011

Number Theory Level 3

Find the number of ordered pairs ( x , y ) (x,y) of real numbers such that 1 6 x 2 + y + 1 6 x + y 2 = 1 \large 16^{x^2 + y} + 16^{x+y^2} = 1 .


The answer is 1.

Himanshu Gupta by Himanshu Gupta , 21, India

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1 solution

Raushan Sharma
Jan 29, 2016

( − 1 2 , − 1 2 ) (\frac{-1}{2}, \frac{-1}{2}) is one only solution, we can get that by AM-GM inequality. So, the correct answer should be 1.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks. I have updated the answer to 1.

Calvin Lin Staff - 4 years, 8 months ago

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