Question

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

Answer 1

Given : a - b = 4 and ab = 21

On Cubing a - b = 4 both sides, we get

(a - b)³ = (4)³

(a)³– (b)³ – 3 ab (a – b) = 64

[By Using an identity ,  (a - b)³ = a³ - b³ - 3ab(a - b)]

a³ - b³ – 3 × 21(4) = 64

[a - b = 4 and ab = 21]

a³ - b³– 63 x 4 = 64

a³ - b³– 252 = 64

a³ - b³ = 64 + 252

a³ - b³ = 316

Hence, the value of a³ - b³ is 316.

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Answer 2

Answer:

★ a³ – b³ = 216 ★

Step-by-step explanation:

Given:

• a – b = 4
• ab = 21

To Find:

• Value of a³ – b³

Solution:

★( a – b )³= a³ – b³ –3ab ( a – b) ★

→ Cubing on both sides ←

$\small\implies{\sf }$ (a – b)³ = 4³

$\small\implies{\sf }$ a³ – b³ –3ab(a–b) = 64

$\small\implies{\sf }$ a³ – b³ –3 x 21 ( 4) = 64

$\small\implies{\sf }$ a³ – b³ –63(4) = 64

$\small\implies{\sf }$ a³ – b³ – 252 = 64

$\small\implies{\sf }$ a³ – b³ = 64 + 252

$\small\implies{\sf }$ a³ – b³ = 316

Hence, Value of a³–b³ = 316