y-2-x-2-2-x-2-y-Find-the-possible-greatest-value-of-x-y-

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 \dots . . 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 ?