If a = √7 + 2√12 and b = √7

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If a = √7 + 2√12 and b = √7 - 2√12 , then ( a³ + b³ ) is equal to

1. 40
2. 44
3. 48
4. 52

Correct Option: D

a = √7 + 2 × √4 × √3
= √4 + 3 + 2 × 2 × √3
= √( 2 + √3 )² = 2 + √3
∴ b = √7 - 2√12 = 2 - √3
⇒ a + b = 2 + √3 + 2 - √3 = 4
ab = (2 + √3)(2 - √3) = 1
∴ a³ + b³ = ( a + b )³ - 3ab(a + b)
= 64 – 3 × 4 = 52