Prove that if \(a,b\) and \(c\) are positive real numbers then

\(\displaystyle\sqrt{a^2 + b^2 - \sqrt{2}ab} + \sqrt{b^2 + c^2 - \sqrt{2}bc} > \sqrt{a^2 + c^2}\)

If you're stuck, take a closer look at the expressions on the left-hand side.

Prove that if \(a,b\) and \(c\) are positive real numbers then

\(\displaystyle\sqrt{a^2 + b^2 - \sqrt{2}ab} + \sqrt{b^2 + c^2 - \sqrt{2}bc} > \sqrt{a^2 + c^2}\)

If you're stuck, take a closer look at the expressions on the left-hand side.

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## Comments

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TopNewestNice: a rectangular triangle... – Carlos Nehab · 1 year, 11 months ago

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Hint: Hmm... The left hand side sure looks a lot like LoC...

Although, @Sanchayapol Lewgasamsarn , did you mean \(\sqrt{a^2+c^2}\) instead of \(\sqrt{a^2+b^2}\)? – Daniel Liu · 2 years, 9 months ago

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You're on the right approach! – Sanchayapol Lewgasamsarn · 2 years, 9 months ago

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