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

As we know from the algebra formula,
(a – b)³ = a³ – b ³ – 3ab (a – b) .......................(1)
As per given question,
a³ – b ³ = 56 and a – b = 2
Put these value in above equation (1) . We will get,
⇒ 2³ = 56 – 3ab x 2
⇒ 8 = 56 – 3ab x 2
⇒ 8 = 56 – 6ab
⇒ 6ab = 56 – 8 = 48
⇒ ab = 8 ...................... (i)
∴ a² + b² = (a – b)² + 2ab
∴ a² + b² = (a – b)² + 2ab
Put the value of
∴ a² + b² = 2² + 2 x 8
∴ a² + b² = 4 + 16 = 20