Question

If x = √6 + √10, then the value of x + (1/x)
1. (3√6 + 5√10)/4
2. (3√6 - √10)/4
3. (3√6 - 5√10)/4
4. (3√6 + 5)/4

Answer 1

Correct Answer - Option 1 : (3√6 + 5√10)/4

Given

x = √6 + √10

⇒ x = √10 + √6

Calculation

1/x = 1/[√10 + √6] 

⇒ 1/x = 1/[√10 + √6] × [√10 - √6]/[√10 - √6]

⇒ 1/x = [√10 - √6]/(10 - 6)

⇒ 1/x = [√10 - √6]/4

x + 1/x = √10 + √6 + [√10 - √6]/4

⇒ x + 1/x = [4√10 + 4√6 + √10 - √6]/4 

⇒ x + 1/x = [5√10 + 3√6]/4

∴ Value of x + 1/x is [3√6 + 5√10]/4