If a + b + c = 5 and ab + bc + ca = 7, then the value of a3 + b3 + c3 - 3abc is :
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 20.
Given that
If a + b + c = 5 and ab + bc + ca = 7
Formula used
a3 + b3 + c3 - 3abc = ( a + b + c ) ( a 2 + b2 + c2 - bc - ab - ac )
(a + b + c)2 = a2 + b2 + c2 +2(ab +bc + ca)
Calculation
⇒ (5)2 = a2 + b2 + c2 +2(7)
⇒ 25 = a2 + b2 + c2 + 14
⇒ a2 + b2 + c2 = 25 - 14 = 11
Hence, the value of
⇒ a3 + b3 + c3 - 3abc = ( 5) (11 - 7) = 5 × 4 = 20