y^2 + x^2 = 2^x + 2^y Find the possible greatest value of ∣x − y∣


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Question Number 7545 by Tawakalitu. last updated on 03/Sep/16

$y^{2} + x^{2} = 2^{x} + 2^{y}$ $F i n d t h e p o s s i b l e g r e a t e s t v a l u e o f ∣ x - y ∣$
Commented by Yozzia last updated on 03/Sep/16

$2^{x - y} + 1 = 2^{- y} (y^{2} + x^{2})$ $(x - y) l n 2 = l n (2^{- y} (y^{2} + x^{2}) - 1)$ $∣ x - y ∣= \frac{∣ l n (\frac{x^{2} + y^{2}}{2^{y}} - 1) ∣}{l n 2} = \frac{∣ l n (x^{2} + y^{2} - 2^{y}) - y l n 2 ∣}{l n 2}$
Commented by Tawakalitu. last updated on 03/Sep/16

$T h a n k s s i r b u t i t h i n k i t n e e d t o f i n d a n u m e r i c v a l u e . . . . . i m e a n$ $a n u m b e r$
Commented by FilupSmith last updated on 03/Sep/16

$solve for x or y, find global maximum ?$
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