Problem
ALG-B1-M12-P020 Variant 5, Problem 4
#20
★★★★☆ Level 4 of 5
\(f:\mathbb Q\to\mathbb Q\), \(f(x+y)=f(x)+f(y)+2xy\), \(f(1)=1\). Find \(f\).
Subtract \(x^2\).
\(g(x)=f(x)-x^2\) is additive, \(g(1)=0\), hence \(g=0\). Answer: \(f(x)=x^2\).
Mock olympiad problem. Tags: functional-equation.