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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, 8 months ago

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Nice: a rectangular triangle...

- 2 years, 8 months ago

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 $$\sqrt{a^2+b^2}$$?

- 3 years, 7 months ago

Oh Thank you. That was really kind of you.

You're on the right approach!

- 3 years, 7 months ago