Math Question and Answers


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 195511 by Calculusboy last updated on 04/Aug/23

	Answered by mr W last updated on 04/Aug/23

	$t h e r e a r e i n f i n i t e v a l u e s f o r k + 1 .$ $c u r v e x^{y} + y^{x} = 8 i s s y m m e t r i c a b o u t$ $y = x . s a y i t p a s s e s t h e p o i n t (a, a),$ $t h e n 2 a^{a} = 8 \Rightarrow a = 2 .$ $s t r a i g h t l i n e x + y = k^{2} i n t e r s e c t s t h e$ $c u r v e x^{y} + y^{x} = 8 i f k^{2} ⩾ a + a = 4, i . e .$ $i f k ⩽ - 2 o r k ⩾ 2 . s o w e h a v e$ $k + 1 ⩽ - 1 o r k + 1 ⩾ 3$
	Commented by Calculusboy last updated on 04/Aug/23

	$t h a n k s s i r$
	Commented by kapoorshah last updated on 05/Aug/23

	$p r o o f t h a t x^{y} + y^{x} = 8 i s s y m m e t r i c$ $a b o u t y = x$
	Commented by mr W last updated on 05/Aug/23

	${i t}^{'} s o b v i o u s . w h e n y o u r e p l a c e x w i t h$ $y a n d y w i t h x, d o y o u g e t t h e s a m e ?$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum