Waste less time on Facebook — follow Brilliant.

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, 2 months ago

No vote yet
1 vote


Sort by:

Top Newest

Nice: a rectangular triangle... Carlos Nehab · 2 years, 3 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 · 3 years, 1 month ago

Log in to reply

@Daniel Liu Oh Thank you. That was really kind of you.

You're on the right approach! Sanchayapol Lewgasamsarn · 3 years, 1 month ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...