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Question Number 175108 by Mastermind last updated on 19/Aug/22

	Answered by MJS_new last updated on 19/Aug/22
	$y=px { (((p^4 +6p^2 +1)x^4 =1)),(((p+1)^4 x^5 =x(1−p))) :} x=0 ⇒ no solution for y { ((x^4 =(1/(p^4 +6p^2 +1)))),((x^4 =((1−p)/((p+1)^4 )))) :} (1/(p^4 +6p^2 +1))=((1−p)/((p+1)^4 )) p(p^4 +10p^2 +5)=0 ⇒ p=0 ⇒ y=0 ⇒ x=±1$
	$y = p x$ ${\begin{cases} (p^{4} + 6 p^{2} + 1) x^{4} = 1 \\ {(p + 1)}^{4} x^{5} = x (1 - p) \end{cases}$ $x = 0 \Rightarrow no solution for y$ ${\begin{cases} x^{4} = \frac{1}{p^{4} + 6 p^{2} + 1} \\ x^{4} = \frac{1 - p}{{(p + 1)}^{4}} \end{cases}$ $\frac{1}{p^{4} + 6 p^{2} + 1} = \frac{1 - p}{{(p + 1)}^{4}}$ $p (p^{4} + 10 p^{2} + 5) = 0$ $\Rightarrow p = 0 \Rightarrow y = 0 \Rightarrow x = \pm 1$
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