Algebra

Algebra Level 4

Find the number of real ordered pairs ( x , y ) (x,y) for which

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

0 1 2 3

Addanki Raghavendra by Addanki Raghavendra , 19, India

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1 solution

Aaghaz Mahajan
May 14, 2018

Simply use AM-GM.......and then complete the squares in the exponents........we see that the minimum of LHS is equal to one........and hence equality holds when x = y = -0.5

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes, thats right

Addanki Raghavendra - 3 years ago

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My pleasure......

Aaghaz Mahajan - 3 years ago

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