x,y are rational numbers where x≠0, y≠0, x≠y, then is it possible: x^5 +y^5 =2x^2 y^2 ?


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 211954 by RojaTaniya last updated on 25/Sep/24

$x, y a r e r a t i o n a l n u m b e r s w h e r e$ $x \neq 0, y \neq 0, x \neq y, t h e n i s i t$ $p o s s i b l e : x^{5} + y^{5} = 2 x^{2} y^{2} ?$
	Answered by Frix last updated on 25/Sep/24

	$x^{5} - 2 x^{2} y^{2} + y^{5} = 0$ $y = p x$ $(p^{5} + 1) x^{5} - 2 p^{2} x^{4} = 0$ $(p^{5} + 1) x - 2 p^{2} = 0$ $x = \frac{2 p^{2}}{p^{5} + 1} \Rightarrow y = \frac{2 p^{3}}{p^{5} + 1}$ $p \in Q \Rightarrow (x, y) \in Q^{2}$
	Commented by RojaTaniya last updated on 25/Sep/24

	$S i r p e r f e c t .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum