Question

If \((x- \frac{1}{2})^2 -(x-\frac{3}{2})^2=x + 2,\) then the value of x is:
1. 4
2. 6
3. 2
4. 8

Answer 1

Correct Answer - Option 1 : 4

Given:

The expression is \((x- \frac{1}{2})^2 -(x-\frac{3}{2})^2=x + 2,\)

Concept:

a² - b² = (a + b) × (a - b)

Calculation:

⇒ (x - 1/2 + x - 3/2) × (x - 1/2 - x + 3/2) = x + 2

⇒ (2x - 2) × (1) = x + 2

⇒ x = 4

∴ The required result will be 4.