e=2 Proof: Let x=((e+2)/2) 2x=e+2 2x(e−2)=(e+2)(e−2) 2ex−4x=e^2 −4 −4x+4=−2ex+e^2 x^2 −4x+4=x^2 −2ex+e^2 (x−2)^2 =(x−e)^2 (√((x−2)^2 ))=(√((x−e)^2 )) x−2=x−e −2=−e e=2


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Question Number 203035 by Frix last updated on 07/Jan/24

$e = 2$ $Proof :$ $Let x = \frac{e + 2}{2}$ $2 x = e + 2$ $2 x (e - 2) = (e + 2) (e - 2)$ $2 e x - 4 x = e^{2} - 4$ $- 4 x + 4 = - 2 e x + e^{2}$ $x^{2} - 4 x + 4 = x^{2} - 2 e x + e^{2}$ ${(x - 2)}^{2} = {(x - e)}^{2}$ $\sqrt{{(x - 2)}^{2}} = \sqrt{{(x - e)}^{2}}$ $x - 2 = x - e$ $- 2 = - e$ $e = 2$
Commented by Calculusboy last updated on 07/Jan/24

$n i c e s i r$
Commented by deleteduser1 last updated on 07/Jan/24

$2 x = e + 2 \Leftrightarrow 2 x (e - 2) = (e + 2) (e - 2) i s o n l y v a l i d$ $w h e n e \neq 2$ $\sqrt{{(x - 2)}^{2}} = \sqrt{{(x - e)}^{2}} \Rightarrow x - 2 = x - e i s o n l y v a l i d$ $w h e n x ⩾ 2 \land x ⩾ e$ $e h e r e a l s o h a s n o t h i n g t o d o w i t h {E u l e r}^{'} s$ $n u m b e r (\approx 2.718281) . S o, i t i s a c t i n g l i k e a$ $r a n d o m v a r i a b l e . I t c o u l d a l s o b e a, b, s, t, x . . .$
Commented by Frix last updated on 08/Jan/24
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