If (a + b + c) = 12, and (a2 + b2+ c2) = 50, find the value of (a3 + b3 + c3 - 3abc).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 36.
We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
⇒ 122 - 50 = 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 144 - 50 = 94
⇒ (ab + bc + ca) = 47
Now, we know that,
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab + bc + ca)
⇒ 12 × (50 - 47)
⇒ 12 × 3
⇒ 36