solve-for-x-e-2x-2e-x-1-0-

Question Number 38957 by Rio Mike last updated on 01/Jul/18

s o l v e f o r x

e^{2 x} + 2 e^{x} + 1 = 0

Commented by math khazana by abdo last updated on 02/Jul/18

i f x f r o m R (e) \Leftrightarrow {(e^{x} + 1)}^{2} = 0 \Leftrightarrow e^{x} + 1 = 0

\Leftrightarrow e^{x} = - 1 ? \Rightarrow n o ? s o l u t i o n .

i g x f r o m C (e) \Leftrightarrow e^{x} + 1 = 0 \Leftrightarrow e^{x} = - 1 \Leftrightarrow

e^{x} = e^{i (2 k + 1) π} \Leftrightarrow x_{k} = i (2 k + 1) π k \in Z

t h e c o m p l e x x_{k} a r e s o l u t i o n s .

Answered by tanmay.chaudhury50@gmail.com last updated on 01/Jul/18

{(e^{x} + 1)}^{2} = 0 w h e n e^{x} = - 1

e^{x} = e^{i Π}

x = i Π

{e^{i Π} = c o s Π + i s i n Π = c o s Π + i s i n Π = - 1}

Commented by MJS last updated on 01/Jul/18

true but not complete

x = (2 z + 1) π i; z \in Z

Commented by tanmay.chaudhury50@gmail.com last updated on 02/Jul/18

y e s s i r i p u t t h e p r i n i c i p a l v a l u e o n l y