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If a + b = 4, and ab = 3, then what is the value of a3 + b3 = ?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
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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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Summary:
If a + b = 4, and ab = 3, then what is the value of a3 + b3 = ?
The value of a3 + b3 = 28 if a + b = 4, and ab = 3. The value is calculated using (a3 + b3) = (a + b) (a2 + b2 – ab)
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