Solve for x : (x − (1/x))^(1/2) + (1 − (1/x))^(1/2) = x


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Question Number 191675 by MATHEMATICSAM last updated on 28/Apr/23

$Solve for x :$ ${(x - \frac{1}{x})}^{\frac{1}{2}} + {(1 - \frac{1}{x})}^{\frac{1}{2}} = x$
Commented by mehdee42 last updated on 29/Apr/23

$t h e g r a p h o f t h e f u n c t i o n i s a s f o l l o w s . t h e r e f o r e . t h e g i v e n$ $e q u a t i o n h a s o n l y o n e r o o t i n t h e$ $i n t e r v a l (1, 2)$
Commented by mehdee42 last updated on 29/Apr/23

	Answered by manxsol last updated on 30/Apr/23

	$x > 0$ $\frac{x - 1}{x} ≫ 0 + \overset{o}{0} - \overset{∙}{1} +$ $x ⩾ 1$ $\frac{x^{2} - 1}{x} ≫ 0 - - \overset{∙}{1} + \overset{o}{0} - \overset{∙}{1} +$ $x ≫ 1$ $s o l i n e c u a c i o n x ⩾ 1$
	Commented by mehdee42 last updated on 28/Apr/23

	$x ⩾ 0, \frac{x - 1}{x} ⩾ 0 \Rightarrow x ⩾ 1$
	Answered by Frix last updated on 29/Apr/23

	$x = \frac{1 + \sqrt{5}}{2}$ $x - \frac{1}{x} = 1$ $1 - \frac{1}{x} = \frac{1}{x^{2}}$
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