If (a + b + c) = 12, and (ab + bc + ca) = 47, find the value of (a³ + b3 + c3 - 3 abc).
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 36.
Given that
If (a + b + c) = 12, and (ab + bc + ca) = 47,
Formula used
(a³ + b3 + c3 - 3 abc) = (a + b +c)(a2 + b2 + c2 – ab – bc – ca)
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
Calculation
⇒ (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
⇒ (12)2 = a2 + b2 + c2 + 2 × 47
⇒ a2 + b2 + c2 = 144 - 94 = 50
Hence, (a³ + b3 + c3 - 3 abc) = 12 (50 - 47) = 12 × 3 = 36