If a3 + b3 = 9 and a + b = 3, then the value of 1 + 1 is

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If a³ + b³ = 9 and a + b = 3, then the value of 1 + 1 is :
a b

1. 1
  2
2. 1
  3
3. 2
  5
4. 5
  6

Correct Option: B

a³ + b³ = (a + b)(a² - ab + b²)
⇒ 9 = 3(a² - ab + b²) { ∴ a + b = 3 }
⇒ a² - ab + b² = 9 ÷ 3 = 3
⇒ (a - b)² – 2ab – ab = 3
⇒ 9 – 3ab = 3
⇒ 3ab = 9 – 3 = 6
⇒ ab = 2

∴	1	+	1	=	a + b	=	3
	a		b		ab		2