If a + b + c = 2 and ab + bc + ca = -1, then the value of a3 + b3 + c3 - 3abc is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 14.
a3 + b3 + c3- 3abc = (a + b + c) {(a2+b2+c2) - (ab + bc + ca)}
=>a3 + b3 + c3- 3abc = (a + b + c) {(a + b + c)2 - 3(ab + bc + ca)}
=>a3 + b3 + c3- 3abc = 2 × {(2)2 - 3 × (-1)}
=>a3 + b3 + c3- 3abc = 2 × (4 + 3 )
=>a3 + b3 + c3- 3abc = 14