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(3x-1)^2/x+(3y-1)^2/y >=1, for x,y>0, x+y=1 Austria Beginners' 2010 p3

Source:

October 3, 2021

function

Problem Statement

Let

x

and

y

be positive real numbers with

x + y =1

. Prove that

\frac{(3x-1)^2}{x}+ \frac{(3y-1)^2}{y} \ge1.

For which

x

and

y

equality holds?
(K. Czakler, GRG 21, Vienna)