lean_workbook_plus_22326

Apply Cauchy-schwarz inequality on $\left(\frac{x}{\sqrt{a}},\sqrt{a}\right)$ and similarly, $y,b$ instead of $x,a$ \n $\left(\frac{x^2}{a}+\frac{y^2}{b}\right)(a+b)\geq (x+y)^2\implies \frac{x^2}{a}+\frac{y^2}{b}\geq\frac{(x+y)^2}{a+b}$