Question

If `2^(2x + 2) - 5 * 2^x + 1 = 0`, then the value of x is ______.

Options

• 0

• 1

• –1

• 2

Answer 1

If `2^(2x + 2) - 5 * 2^x + 1 = 0`, then the value of x is 0.

Explanation:

We are given:

`2^(2x + 2) - 5 * 2^x + 1 = 0`

Step 1: Use the exponent rule:

`2^(2x + 2) = 2^2 * (2^x)^2`

`2^(2x + 2) = 4 * (2^x)^2`

Let y = 2^x, so the equation becomes:

4y² – 5y + 1 = 0

Step 2: Solve the quadratic:

4y² – 5y + 1 = 0

⇒ `y = (5 +- sqrt((-5)^2 - 4 * 4 * 1))/(2 * 4)`

⇒ `y = (5 +- sqrt(25 - 16))/8`

⇒ `y = (5 +- 3)/8`

⇒ y = 1 

or

⇒ `y = 1/4`

Step 3: Recall y = 2^x

So, If 2^x = 1 ⇒ x = 0

If `2^x = 1/4` ⇒ x = –2

Only x = 0 is among the options.