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minimum of f(a, b) + f (a,-b) + f(-a, b) + f (-a, -b)

Source: Bulgaria JBMO TST 2018, Day 2, Problem 1

June 25, 2018
inequalities2018

Problem Statement

For real numbers aa and bb, define f(a,b)=a2+b2+26a+86b+2018.f(a,b) = \sqrt{a^2+b^2+26a+86b+2018}. Find the smallest possible value of the expression f(a,b)+f(a,−b)+f(−a,b)+f(−a,−b).f(a, b) + f (a,-b) + f(-a, b) + f (-a, -b).
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