Question

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

Answer 1

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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

Step-by-step explanation:

a - b = 4

ab = 21

$a^{3} -b^{3} =(a-b)(a^{2} +ab+b^{2} )$

$(a-b)^{2} =(4)^{2}\\a^{2} -2ab+b^{2} =16\\a^{2} -2(21)+b^{2} =16\\a^{2} -42+b^{2} =16\\a^{2} +b^{2} =42+16\\Therefore, a^{2} +b^{2} =58$

Substituting the values-

$a^{3} -b^{3} =(4)(21+58 )$

= 4*79

=316

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