Question Number 94654 by msup by abdo last updated on 20/May/20
$${prove}\:{that}\:\sum_{{i}=\mathrm{1}} ^{{n}} \:{x}_{{i}} {y}_{{i}} \leqslant\left(\sum_{{i}=\mathrm{1}} ^{{n}} {x}_{{i}} ^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \left(\sum_{{i}=\mathrm{1}} ^{{n}} {y}_{{i}} ^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$${x}_{{i}} \:{and}\:{y}_{{i}} \:{reals}\:\geqslant\mathrm{0} \\ $$