how-to-prove-x-y-y-x-1-x-y-R-x-y-gt-0-

Question Number 76290 by benjo last updated on 26/Dec/19

how to prove x^{y} + y^{x} ⩾ 1, x, y \in R

x, y > 0

Commented by MJS last updated on 26/Dec/19

we can exchange x and y \Rightarrow let x ⩽ y

{it}^{'} s easy for these cases

(1) x = y

(2) 1 ⩽ x < y < \infty

(3) 0 < x ⩽ 1 < y < \infty

I found no proper way for

(4) 0 < x < y < 1

Answered by mind is power last updated on 26/Dec/19

x = y = - 3 false

Commented by benjo last updated on 26/Dec/19

sir x > 0 and y > 0

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