. If a – b = 3 and a3 - b3 = 117 then |a + b| is equal

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. If a – b = 3 and a³ - b³ = 117 then |a + b| is equal to

1. 3
2. 5
3. 7
4. 9

Correct Option: C

a – b = 3
a³ - b³ = 117
a³ - b³ = ( a - b )³ + 3ab (a – b)
⇒ 117 = 27 + 3ab (3)
⇒ 9ab = 117 – 27 = 90
⇒ ab = 10
∴ ( a + b )² = ( a - b )² + 4ab
= 9 + 40 = 49
∴ |a + b| = 7