Question

If \(2 = x + \frac 1 {1 + \frac 1 {5 + \frac 1 2}},\) then the value of x is equal to:
1. 1
2. \(\frac {13}{15}\)
3. \(\frac {15}{13}\)
4. \(\frac {14}{13}\)

Answer 1

Correct Answer - Option 3 : \(\frac {15}{13}\)

Given:

\(2 = x + \frac 1 {1 + \frac 1 {5 + \frac 1 2}}\)

Calculations:

\(2 = x + \frac 1 {1 + \frac 1 {5 + \frac 1 2}}\)

⇒ \(2 = x + \frac 1 {1 + \frac 2 {11}}\)

⇒ 2 = x + 11/(11 × 1 + 2)

⇒ 2 = x + 11/13

⇒ x = 2 – 11/13

⇒ x = 15/13

∴ The value of x is 15/13.