If a + b = 4, and ab = 3, then what is the value of a3 + b3 = ?

By K Balaji|Updated : October 6th, 2022
  1. 9
  2. 35
  3. 28
  4. 20

If a + b = 4, and ab = 3, then the value of a3+ b3 = 28

Given: a + b = 4, ab = 3

We know that,

(a + b)2 = a2 + b2 + 2ab

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

By using this

(a + b)2 = a2 + b2 + 2ab

By substituting

⇒ (4)2 = a2 + b2 + 2 × 3

⇒ a2 + b2 = 10 … (1)

⇒ (a3 + b3) = (4) × (10 - 3)

⇒ (a3 + b3) = 28

Therefore, the required result will be 28.

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