If (x - 1/x ) = 0.4 and x > 0, what is the value of (x² + 1/(x²) ) ?

If (x - 1/x ) = 0.4 and x > 0, what is the value of (x² +…

If (x - $\frac{1}x$ ) = 0.4 and x > 0, what is the value of (x² + $\frac{1}{x^2}$ ) ?

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 2.16.

x - (1/x) = 0.4

⇒ [x - (1/x)]² = 0.4² = 0.16 [Squaring both sides]

⇒ x² - [2 × x × (1/x)] + (1/x)² = 0.16

⇒ x² - 2 + (1/x)² = 0.16

⇒ x² + (1/x)² = 0.16 + 2 = 2.16

Therefore, the required value is 2.16.