Problem #PRU-66357

Problems Algebra Surds. Rational powers Irrational inequalities.

Problem

It is known that $a = x + y + \sqrt{x y}$ , $b = y + z + \sqrt{y z}$ , $c = x + z + \sqrt{x z}$ . where $x > 0$ , $y > 0$ , $z > 0$ . Prove that $a + b + \sqrt{a b} > c$ .

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