Question

Solve $2^{2x+2}-6\times 2^x+2=0$

• A. $x=-1orx=0$
• B. $x=-1orx=1$
• C. $x=-1orx=2$
• D. $x=-2orx=0$

Answer 1

The correct option is A

$x=-1orx=0$

Given $2^{2x+2}-6\times 2^x+2=0$

$\Rightarrow$ $2^{2x}\times 2^2-6\times 2^x+2=0$

$\Rightarrow$ $4(2^x{)}^2-6(2^x)+2=0$

$\Rightarrow$ $4y^2-6y+2=0$ [let $2^x=y$]

Solving the quadratic equation we get

$(4y-2)(y-1)$

$\Rightarrow y=\frac{1}{2}or1$

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

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