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\sqrt{a^2+b^2+2}+\sqrt{b^2+c^2+2 }+\sqrt{c^2+a^2+2}\ge 6

Source: JBMO Shortlist 2017 A1

July 25, 2018
algebraInequalityreal number3-variable inequality

Problem Statement

Let a,b,ca, b, c be positive real numbers such that a+b+c+ab+bc+ca+abc=7a + b + c + ab + bc + ca + abc = 7. Prove that a2+b2+2+b2+c2+2+c2+a2+2≥6\sqrt{a^2 + b^2 + 2 }+\sqrt{b^2 + c^2 + 2 }+\sqrt{c^2 + a^2 + 2 } \ge 6 .
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