Problem
ALG-B2-M03-P002 Two fractions
#2
★★☆☆☆ Level 2 of 5
For \(p,q>0\), prove \(\frac{x^2}{p}+\frac{y^2}{q}\ge\frac{(x+y)^2}{p+q}\).
Hint 1. Use Engel form.
Hint 2. Positive denominators allow the fractions to be combined.
By Engel form, \(\frac{x^2}{p}+\frac{y^2}{q}\ge\frac{(x+y)^2}{p+q}\). Equality occurs when \(\frac{x}{p}=\frac{y}{q}\).
Cauchy-Schwarz module training problem. Method tags: cauchy, engel-form.