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If a3 + b3 = 16 and (a + b)3 = 64 find ab

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If a3 + b3 = 16 and (a + b)3 = 64 find ab


1. 4
2. 6
3. 8
4. 2
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Correct Answer - Option 1 : 4

Given

a3 + b3 = 16

(a + b)3 = 64

Formula used

(a + b)3 = a3 + b3 + 3ab(a + b)

Calculation

If (a + b)3 = 64 then, (a + b) = 4

64 = 16 + 3ab(4)

⇒ 64 - 16 = 3ab(4)

⇒ 48 = 3ab(4)

⇒ 12ab = 48

⇒ ab = 4

∴ Value of ab is 4

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