Subject: Re: Cauchy's inequality
Date: Wed, 26 Nov 1997 09:35:56 -0500
From: Alex Bogomolny
Congratulations on your success in math competition. The easiest way to prove Cauchy's Inequality is this. Let x be just a variable. Write
sum of (x*ai + bi)2 =
and open parentheses. The result is a quadratic polynomial in x. Note that, by definition, this polynomial is never negative. This implies that its discriminant (the expression under the square root in the formula for its two roots) is non-negative. This is exactly the Cauchy's inequality.