Just the right Percentage.

Algebra Level 4

{ a 2 + b 2 < 16 a 2 + b 2 < 8 a a 2 + b 2 < 8 b \large \begin{cases} a^2 + b^2 < 16 \\ a^2 + b^2 < 8a\\ a^2 + b^2 < 8b \end{cases}

How many ordered pairs of integers ( a , b ) (a,b) satisfy the above system of inequalities?


The answer is 6.

Samara Simha Reddy by Samara Simha Reddy , 22, India

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1 solution

( 1 , 2 ) (1, 2) ( 2 , 1 ) (2, 1) ( 1 , 1 ) (1, 1) ( 2 , 2 ) (2, 2) ( 3 , 2 ) (3, 2) ( 2 , 3 ) (2, 3)

It is clear neither can be negative or 0.

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