Question

`{2}^(x) - 3( {2}(^(x) + (1)/(2) )) + {2}^(2) = 0`

Can someone solve this equation?​

Answer 1

Answer:
`\huge\boxed{x=log_2(12√(2)+4)/(17)}`

Step-by-step explanation:
`\displaystyle\ \bigg{2^x-3(2^{x+(1)/(2) }})+2^2=0 \qquad ; \ \ \boxed{t=2^x} \\\\t-3t√(2) +4=0 \\\\ t(1-3√(2) )=-4 \\\\ t=(4)/(3√(2) -1) \cdot (3√(2)+1 )/(3√(2)+1 ) =(12√(2)+4)/(17) \\\\\\2^x=(12√(2)+4)/(17) \\\\x=log_2 \ \ (12√(2)+4)/(17)`