solve for x and y in this equation x^x +y^y =31 x+y=5


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Question Number 11543 by Nysiroke last updated on 28/Mar/17

$s o l v e f o r x a n d y i n t h i s e q u a t i o n$ $x^{x} + y^{y} = 31$ $x + y = 5$
	Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 29/Mar/17

	$x a n d y a r e n o t b o t h e v e n o r o d d . b e c a u s e$ $t h e s u m o f t w o e v e n o r t w o o d d n u m b e r$ $c a n n o t b e e q u a i l t o 5 . s o f o r o n e o f x o r$ $y s h o u l d b e e v e n a n d o n e b e o d d .$ $l e t : x = 2 p + 1 a n d y = 2 q .$ $2 p + 1 + 2 q = 5 \Rightarrow 2 (p + q) = 4 \Rightarrow p + q = 2$ $f r o m f i r s t e q u a t i o n, x a n d y s h o u l d$ $b e p o s i t i v e n u m b e r s . s o t h e o n l y$ $p o s s i b l e v a l u e f o r p a n d q, i s : p = q = 1$ $\Rightarrow x = 2 \times 1 + 1 = 3, y = 2 \times 1 = 2$ $t h e n : (x, y) = (3, 2) o r (2, 3) .$
	Commented by Nysiroke last updated on 02/Apr/17

	$T h a n k s s o m u c h . G o d b l e s s$
	Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 29/Mar/17

	$(3, 2), (2, 3) .$
	Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 29/Mar/17

	Commented by Nayon last updated on 29/Mar/17

	$c a n y o u g i v e t h e a p p b y w h i c h y o u$ $d r a w n t h e g r a p h ?$
	Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Mar/17

	$g e o g e b r a$
	Commented by Nysiroke last updated on 02/Apr/17

	$E x c e l l e n t .$
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