If a3 - b3 = 56 and a – b = 2, then value of a2 + b2

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If a³ - b³ = 56 and a – b = 2, then value of a² + b² will be :

1. 48
2. 20
3. 22
4. 5

Correct Option: B

Using Rule 9,
a³ - b³ = 56
⇒ (a – b)( a² + ab + b² ) = 56
⇒ a² + ab + b² = 28
⇒ (a – b)² + 3ab = 28
⇒ 4 + 3ab = 28
⇒ 3ab = 28 – 4 = 24
⇒ ab = 8
∴ a² + b² = (a – b)² + 2ab
= 4 + 16 = 20