Question

Solve $2^{2x+3}-9\times 2^x+1=0$

• A. $x=-3orx=3$
• B. $x=3orx=0$
• C. $x=-3orx=0$
• D. $x=-2orx=0$

Answer 1

The correct option is C

$x=-3orx=0$

Given $2^{2x+3}-9\times 2^x+1=0$

$\Rightarrow$ $2^{2x}\times 2^3-9\times 2^x+1=0$

$\Rightarrow$ $8(2^x{)}^2-9(2^x)+1=0$

$\Rightarrow$ $8y^2-9y+1=0$ [let $2^x=y$]

Solving the quadratic equation we get

$(8y-1)(y-1)$

$\Rightarrow y=\frac{1}{8}or1$

When $y=\frac{1}{8}$ $\Rightarrow 2^x=2^{-3}\Rightarrow x=-3$

When $y=1\Rightarrow 2^x=1\Rightarrow x=0$