Question

If x = √6 + √5 and y = √6 - √5, then find the value of (x³ – 5√5) – (y³ - √5).

1. 46√5
2. 42√5
3. 41√5
4. 40√5

Answer 1

Correct Answer - Option 2 : 42√5

Given:

x = √6 + √5

y = √6 - √5

Formula used:

(x³ – y³) = (x – y)³ + 3xy(x – y)

(x² – y²) = (x – y) (x + y)

Calculation:

x – y = (√6 + √5) – (√6 - √5)

⇒ x – y = 2√5

Now, we have to find the value of 

(x³ – 5√5) – (y³ – √5)

⇒ x³ - y³ - 4√5

⇒ (x – y)³ + 3xy(x – y) – 4√5

⇒ (2√5)3 + 3 × (√6 + √5) × (√6 – √5) × 2√5 – 4√5 

⇒ 40√5 + 3 × (√6 + √5) × (√6 – √5) × 2√5 – 4√5

⇒ 40√5 + 3 × {(√6)² – (√5)²} × 2√5 – 4√5

⇒ 40√5 + 3 × 2√5 – 4√5

⇒ 42√5

∴ The value of (x³ – 5√5) – (y³ – √5) is 42√5.