Prove that for all positive real numbers , .
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Originally Posted by Sigyn3 Prove that for all positive real numbers , . by AM-GM we have thus: so we only need to prove that let then (1) becomes which is obviously true because
Another solution. By AM–GM, . Similarly . And . Adding up,
here's a general form of the inequality that i just made it up: suppose are positive real numbers with prove that for all positive real numbers
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