Let be the sides of a triangle. Prove that Always Try A Substitution We notice that the denominators are all positive, in fact by the triangular inequality. So let . Then . So we get applying in the last step. Similarly, we obtain Thus, now it is sufficient to prove that So let’s assume WLOG […]

# Tag: Inequality

## Cauchy-Schwarz And Titu Inequalities

Today I’m going to show two very nice inequalities to know, which really are useful in the mathematical olympiads. What They Say And Their Proof The Cauchy-Schwarz inequality asserts that, for real tuples we have: Here’s the proof: consider the expression It’s obviously true since each term of the sum is non negative. Hence we […]