Question

if 2^2x-1 + 2^1-2x = 2 then x = ?
plz tell with full explanation ​

Answer 1

GIVEN :–

$\\ \: \: \: { \bold{.}} \: \: \: { \bold{ {2}^{2x - 1} + {2}^{1 - 2x} = 2}}$

TO FIND :–

• value of 'x' = ?

SOLUTION :–

$\\ \implies{ \bold{ {2}^{2x - 1} + {2}^{1 - 2x} = 2}}$

$\\ \implies{ \bold{ {2}^{2x - 1} + {2}^{ - (2x - 1)} = 2}}$

• Let's put $\: \: { \bold{ {2}^{2x - 1} = t \: \: - }}$

• So that –

$\\ \implies{ \bold{ t + {t}^{ - 1} = 2}}$

$\\ \implies{ \bold{ t + \dfrac{1}{t} = 2}}$

$\\ \implies{ \bold{ {t}^{2} + 1 = 2t}}$

$\\ \implies{ \bold{ {t}^{2} - 2t + 1 = 0}}$

$\\ \implies{ \bold{ {(t - 1)}^{2} = 0}}$

$\\ \implies{ \bold{ t = 1}}$

• Now replace 't' –

$\\ \implies{ \bold{ {2}^{2x - 1} = 1}}$

• We should write this as –

$\\ \implies{ \bold{ {2}^{2x - 1} = {2}^{0} }}$

• Now compare –

$\\ \implies{ \bold{ {2x - 1} = 0 }}$

$\\ \implies{ \bold{ {2x } = 1 }}$

$\\ \: \: \longrightarrow \: \large { \boxed{ \bold{ {x } = \dfrac{1}{2} }}}$