An algebra problem by Wildan Bagus Wicaksono

Algebra Level 2

Given x x and y y are real numbers that satisfy x 2 + y 2 = 1 { x }^{ 2 }+{ y }^{ 2 }=1 . Determine the largest possible x y xy value.


The answer is 0.5.

Wildan Bagus Wicaksono by Wildan Bagus Wicaksono , 18, Indonesia

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1 solution

Based on A M ≥ G M AM\ge GM ,

x 2 + y 2 2 ≥ x 2 y 2 1 2 ≥ x y 0.5 ≥ x y \frac { { x }^{ 2 }+{ y }^{ 2 } }{ 2 } \ge \sqrt { { x }^{ 2 }{ y }^{ 2 } } \\ \frac { 1 }{ 2 } \ge xy\\ 0.5\ge xy

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