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For-x-gt-0-y-lt-1-Prove-that-x-y-y-x-gt-1-

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Question Number 58587 by naka3546 last updated on 25/Apr/19
For x > 0 , y < 1 . Prove that x^y + y^x > 1
$${For}\:\:\:{x}\:>\:\mathrm{0}\:\:,\:\:\:{y}\:\:<\:\:\mathrm{1}\:. \\ $$$${Prove}\:\:{that}\:\:\:\:{x}^{{y}} \:+\:{y}^{{x}} \:\:>\:\:\mathrm{1} \\ $$

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