Question

If 1/√(5 – 2√6) = √A + √B, then find the value of (A² + B²)/26
1. 2
2. 1
3. 1/2
4. 0

Answer 1

Correct Answer - Option 3 : 1/2

Given:

1/√(5 – 2√6) = √A + √B

Concept Used:

(x + y)² = x² + y² + 2xy

Calculations:

√(5 – 2√6) = √((√2)² + (√3)² – 2 × √2 × √3)

⇒ √(5 – 2√6) = √((√3) – √2))²

⇒ √(5 – 2√6) = √3 – √2

1/√(5 – 2√6) = 1/(√3 – √2)

On rationalizing, we get

1/(√3 – √2) × (√3 + √2)/(√3 + √2) 

⇒ (√3 + √2)/(√3)² – (√2)²

⇒ (√3 + √2) = √A + √B

On comparing, we get

A = 3, B = 2

Now, (A2 + B2)/26

Putting value of A and B in this expression,

⇒ (A2 + B2)/26 =(32 + 22)/26

⇒ (A2 + B2)/26 = 13/26

⇒ (A2 + B2)/26 = 1/2

∴ The value of (A2 + B2)/26 is 1/2.