If a + b + c =7, ab + bc + ca = 11 and abc = -1, then a3 + b3+ c3 is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 109.
Given that
If a + b + c = 7, ab + bc + ca = 11 and abc = -1,
Formula used
(a + b + c )2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
a3 + b3 + c3 = (a + b + c ) (a2 + b2 + c2 – ab – bc – ca) + 3abc
Calculation
⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 49
⇒ a2 + b2 + c2 + 2 × 11 = 49
⇒ a2 + b2 + c2 = 49 - 22 = 27
Now,
⇒ a3 + b3 + c3 = 7 (27 - 11) + 3 × (-1)
⇒ a3 + b3 + c3 = 112 - 3 = 109