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Inequality Problem to be Proved!

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.

Note by Sanchayapol Lewgasamsarn
3 years, 4 months ago

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Nice: a rectangular triangle...

Carlos Nehab - 2 years, 5 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 - 3 years, 4 months ago

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Oh Thank you. That was really kind of you.

You're on the right approach!

Sanchayapol Lewgasamsarn - 3 years, 4 months ago

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