If 5x - 1/4x = 6, x > 0, then find the value of 25x² - 1/(16x²) .

If 5x - 1/4x = 6, x > 0, then find the value of 25x²…

If 5x - $\frac{1}{4x}$ = 6, x > 0, then find the value of 25x² - $\frac{1}{16x^2}$ .

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 6 $\sqrt{41}$

Formula used:

(a - b)² = a² + b² - 2ab

(a + b)² = a² + b² + 2ab

(a² - b²) = (a - b)(a + b)

Calculations:

Using equation (1), we get

⇒ (5x - 1/4x)² = 25x² + 1/16x² - 5/2

⇒ 25x² + 1/16x² - 5/2 = 36

⇒ 25x² + 1/16x² = 77/2

Now, we have

⇒ (5x + 1/4x)² = 25x² + 1/16x² + 5/2

⇒ (5x + 1/4x)² = 77/2 + 5/2 = 82/2

⇒ 5x + 1/4x = √41

Now using equation (3), we get

⇒ (5x + 1/4x)(5x - 1/4x)

⇒ 6√41