If a³ – b³ = 56 and a – b = 2, what is the

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If a³ – b³ = 56 and a – b = 2, what is the value of (a² + b²) ?

1. 12
2. 20
3. 28
4. 32

Correct Option: B

a³ – b³ = 56
⇒ (a – b)³ + 3ab (a – b) = 56
⇒ (2)³ + 3ab × 2 = 56
⇒ 6ab = 56 – 8 = 48
⇒ ab = 48 ÷ 6 = 8
∴ a² + b² = (a – b)² + 2ab
= 2²+ 2 × 8
= 4 + 16 = 20