If a – b = 4 and ab = 21, find the value of a3 – b3.

1.	If a – b = 4 and ab = 21, find the value of a3 – b3.
Answer» Given, a – b = 4, ab = 21 Choose a – b = 4 Cubing both sides, (a – b)³ = (4)³ a³ – b³ – 3ab (a – b) = 64 a³ – b³ – 3 × 21 x 4 = 64 a³ – b³ – 252 = 64 a³ – b³ = 64 + 252 a³ – b³ = 316

Answer»

Given,

a – b = 4, ab = 21

Choose a – b = 4

Cubing both sides,

(a – b)³ = (4)³

a³ – b³ – 3ab (a – b) = 64

a³ – b³ – 3 × 21 x 4 = 64

a³ – b³ – 252 = 64

a³ – b³ = 64 + 252

a³ – b³ = 316

Discussion

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