Question

If (3 + √6)x = (3 - √6)z = 2, then the value of (1/x) + (1/z)
1. 9
2. 3
3. 6
4. O

Answer 1

Correct Answer - Option 2 : 3

Given:

(3 + √6)x = (3 - √6)z = 2

Calculation:

(3 + √6)x = 2

⇒ x = 2/(3 + √6).     ----(1)

(3 - √6)z = 2

⇒ z = 2/(3 - √6).     ----(2)

1/x = (3 + √6)/2.     ----(from 1)

1/z = (3 - √6)/2.     ----(from 2)

Adding (1) and (2):

⇒ [(3 + √6)/2] + [(3 - √6)/2]

⇒ (3 + √6 + 3 - √6)/2

⇒ 6/2

⇒ 3

∴ The value of (1/x) + (1/z) is 3.