The value of \(\frac{7+3\sqrt5}{3+\sqrt5}-\frac{7-3\sqrt5}{3-\sqrt{5}

1.	The value of \(\frac{7+3\sqrt5}{3+\sqrt5}-\frac{7-3\sqrt5}{3-\sqrt{5}}\)lies between:1. 1.5 and 22. 3 and 3.53. 2.5 and 34. 2 and 2.5
Answer» Correct Answer - Option 4 : 2 and 2.5 Concept used: a² - b² = (a + b)(a - b) Calculation: \(\frac{7+3√5}{3+√5}-\frac{7-3√5}{3-√{5}}\) ⇒ \( ((7+3√5)(3- √5)- (7-3√5)(3+ √5))/(3+ √5)(3- √5) \) ⇒ (21 + 9√5 - 7√5 - 15 - 21 + 9√5 - 7√5 + 15)/4 ⇒ 4√5/4 = √5 (∵ √5 = 2.236 approx) ⇒ 2.3 (approx) ∴ The value lies between 2 and 2.5.

The value of \(\frac{7+3\sqrt5}{3+\sqrt5}-\frac{7-3\sqrt5}{3-\sqrt{5}}\)lies between:1. 1.5 and 22. 3 and 3.53. 2.5 and 34. 2 and 2.5

Answer» Correct Answer - Option 4 : 2 and 2.5

Concept used:

a² - b² = (a + b)(a - b)

Calculation:

\(\frac{7+3√5}{3+√5}-\frac{7-3√5}{3-√{5}}\)

⇒ \( ((7+3√5)(3- √5)- (7-3√5)(3+ √5))/(3+ √5)(3- √5) \)

⇒ (21 + 9√5 - 7√5 - 15 - 21 + 9√5 - 7√5 + 15)/4

⇒ 4√5/4 = √5

(∵ √5 = 2.236 approx)

⇒ 2.3 (approx)

∴ The value lies between 2 and 2.5.