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If a - b = 3 and a3 - b3 = 189, then find the value of a2 + b2
1. 45
2. 30
3. 70
4. 60

1 Answer

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Correct Answer - Option 1 : 45

Given

a - b = 3

a3 - b3 = 189

Formula used

a3 - b3 = (a - b) (a2+ ab + b2)      ----(1)

(a - b)3 = a3 - b3 - 3ab(a- b)      ----(2)

Calculation

Using (2)

3³ = 189 - 3ab(3)

27 = 189 - 9ab

⇒ ab = 18

Substituting ab = 18 in (1)

189 = 3(a2 + b2 + 18)

⇒ a2 + b2 = 45

∴ a2 + b2 = 45

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