What is the sum of the roots of the equation 4^x – 6·2^x

[Max@Math Revolution]

[GMAT math practice question]

What is the sum of the roots of the equation 4^x - 6·2^x + 8 = 0?

A. 1
B. 3
C. 6
D. 8
E. 12

[deloitte247]

$$4^x-6\cdot2^{x^{ }}+8=0$$
$$\left(4^x-6\right)\cdot\left(2^x+8\right)=0$$
$$2^x=y$$
$$y^2-6\cdot y+8=0$$
$$y^2-6y+8=0$$
$$\left(y^2-4y\right)\left(-2y+8\right)=0$$
$$y\left(y-4\right)-2\left(y-4\right)=0$$
$$y-2=0\ or\ y-4=0$$
Remember that
$$2^x=y\ when\ y=2$$
$$2^x=2$$
$$2^1=2$$
$$x=1$$
when y=4
$$2^x=4$$
$$2^2=4$$
$$x=2$$
Sum of the roots = 2+1 =3

$$Answer\ is\ Option\ B$$

[Max@Math Revolution]

=>

4^x - 6·2^x + 8 = 0
=> (2^x)^2- 6·2^x + 8 = 0
=> (2^x-2)(2^x-4) = 0
=> 2^x = 2 or 2^x = 4
=> 2^x = 2^1 or 2^x = 2^2
=> x = 1 or x = 2

Since 1+2=3, the correct answer is B.
Answer: B