Question

If 5x + 1/7x = 15/7, then find 49x² - 1/25x².

1. √(155/3)
2. √(153/5)
3. √(155/5)
4. √(153/3)
5. √(152/3)

Answer 1

Correct Answer - Option 2 : √(153/5)

Given:

5x + 1/7x = 15/7

Concept used:

(a - b)² = (a + b)² - 4ab

(a + b) (a - b) = a² - b²

Calculation:
5x + 1/7x = 15/7

⇒ (5x + 1/7x) × (7/5) = (15/7) × (7/5)

⇒ 7x + 1/5x = 3

Squaring both sides,

⇒ (7x + 1/5x)² = 9

⇒ (7x + 1/5x)² - 4 × 7x × (1/5x) = 9 - 4 × 7x × (1/5x)

⇒ (7x - 1/5x)² = 9 - 28/5

⇒ (7x - 1/5x)2 = (45 - 28)/5

⇒ 7x - 1/5x = √(17/5)

⇒ 49x² - 1/25x² = (7x + 1/5x) (7x - 1/5x)

⇒ 3 × √(17/5)

⇒ √(153/5)

∴ The value of 49x² - 1/25x² is √(153/5).