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.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestNice: a rectangular triangle... – Carlos Nehab · 1 year, 6 months ago

Log in to reply

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, 5 months ago

Log in to reply

You're on the right approach! – Sanchayapol Lewgasamsarn · 2 years, 5 months ago

Log in to reply