x^((x−1)^2 ) =2x+1 how can it solve this ?help me please


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Question Number 150916 by tabata last updated on 16/Aug/21

$x^{{(x - 1)}^{2}} = 2 x + 1$ $h o w c a n i t s o l v e t h i s ? h e l p m e p l e a s e$
	Answered by MJS_new last updated on 17/Aug/21

	$I {don}^{'} t think we can generally solve$ $x^{{(x - 1)}^{2}} = a x + b$ $but in this special case we can :$ $let t = x - 1 \Leftrightarrow x = t + 1$ ${(t + 1)}^{t^{2}} = 2 t + 3$ $let n = t^{2} \Leftrightarrow t = \pm \sqrt{n}$ ${(1 \pm \sqrt{n})}^{n} = 3 \pm 2 \sqrt{n}$ $obviously n = 2$ $\Rightarrow t = \pm \sqrt{2} \Rightarrow x = 1 \pm \sqrt{2}$
	Commented by tabata last updated on 16/Aug/21

	$t h a n k y o u s i r$
	Commented by tabata last updated on 16/Aug/21

	$a l s o 1 - \sqrt{2} i s s o l u t i o n o f t h i s e q u a t i o n$
	Commented by MJS_new last updated on 17/Aug/21

	$yes, thank you .$
	Commented by otchereabdullai@gmail.com last updated on 22/Aug/21

	$nice$
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