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# a, b and c are positive real numbers. Using only AM-GM (no Jensen, no Holder, no Cauchy-Schwarz, etc) prove that a/√(a² + bc) + b/√(?

a, b and c are positive real numbers. Using only AM-GM (no Jensen, no Holder, no Cauchy-Schwarz, etc) prove that

a/√(a² + bc) + b/√(b² + ca) + c/√(c² + ab) ≥ 1.

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- JOHNLv 75 years ago
Doesn't look like I'll get any solutions to this and the question is shortly due to expire. Here is solution using only algebra and AM - GM.

The 2nd "=" sign in line 5 should be "≤".

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