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a/b + b/c + c/a <= a^2/b^2 + b^2/c^2 + c^2/a^2

Source: Nordic Mathematical Contest 1987 #4

October 5, 2017
inequalitiesalgebraHigh school olympiad

Problem Statement

Let a,ba, b, and cc be positive real numbers. Prove: ab+bc+ca≤a2b2+b2c2+c2a2\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\le \frac{a^2}{b^2} + \frac{b^2}{c^2} + \frac{c^2}{a^2} .
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