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This is for a first year calculus course. Everything I can find online about Cauchy-Schwarz inequalities involves real analysis and vectors etc. I've only just begun calculus.

$x_1$, $x_2$, $y_1$, and $y_2$ are all real numbers.

Prove the Cauchy-Schwarz inequality: $$ x_{1}y_{1}+x_{2}y_{2}\leq \sqrt{x_{1}^{2}+x_{2}^{2}} \sqrt{y_{1}^{2}+y_{2}^{2}}. $$

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    Hint: square both sides, regroup, and compare with the expression $(x_1 y_2 - x_2 y_1)^2$.2011-09-14
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    Look this page http://fatosmatematicos.blogspot.com/2009/08/provas-sem-palavras-parte-4.html2011-09-14
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    you might take the absolute value of the right hand-side. Before it is too late :)2011-09-14

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