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\sqrt{1/(3x+1)}+\sqrt{ (x/x+3)} >=1

Source: 2017 Latvia BW TST P1

December 18, 2022
algebrainequalities

Problem Statement

Prove that for all real x>0x > 0 holds the inequality 13x+1+xx+3≥1.\sqrt{\frac{1}{3x+1}}+\sqrt{\frac{x}{x+3}}\ge 1. For what values of xx does the equality hold?
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