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sum a^2/( b^2 + c^2 ) >=3/2

Source: 1962-63 Germany R4 12.3

October 12, 2024
algebrainequalities

Problem Statement

It has to be proven: If at least two of the real numbers a,b,ca, b, c are different from zero, then the inequality holds a2b2+c2+b2c2+a2+c2a2+b2≥32\frac{a^2}{b^2 + c^2} + \frac{b^2}{c^2 + a^2} + \frac{c^2}{a^2 + b^2} \ge \frac32 Under what conditions does equality occur?
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