Question

If \(\left(x - \dfrac{1}{x}\right)\) = 12, then the value of \(\left(x^2 +\dfrac{1}{x^2}\right)\) is:
1. 146
2. 148
3. 140
4. 144

Answer 1

Correct Answer - Option 1 : 146

Given:

x - (1/x) = 12

Formula used:

(a - b)² = a² + b² - 2ab

Calculation:

According to the formula, we have

{x - (1/x)}² = x² + (1/x)² - 2 × x × (1/x)

⇒ x2 + (1/x)2 - 2 = (12)² 

⇒ x2 + (1/x)2 = 144 + 2 = 146

∴ The value of  x2 + (1/x)2 is 146.