MCQ
If a + b + c = 9 and ab + bc + ca = 23, than a3 + b3 + c3 - 3abc =
- A729
- B207
- C669
- D108
✓
Answer
- 108
Solution:
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
⇒ (9)2 = a2 + b2 + c2 + 2(ab + bc + ca)
⇒ (9)2 = a2 + b2 + c2 + 2(23)
⇒ a2 + b2 + c2 = 81 - 46 = 35
as we know that a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)
⇒ a3 + b3 + c3 - 3abc = 9 × (35 - 23)
⇒ a3 + b3 + c3 - 3abc = 108
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