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x^y+y^x>1, x^x minimum

Source: French MO 1996 P4

April 11, 2021

Inequalityoptimizationinequalities

Problem Statement

(a) A function

f

is defined by

f(x)=x^x

for all

x>0

. Find the minimum value of

f

. (b) If

x

and

y

are two positive real numbers, show that

x^y+y^x>1

.

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