If a + b + c = 9, ab + bc + ca = 26, a3 + b3= 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 24
We know that,
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - ab - ca) .......(1)
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) ......(2)
From (2)
a2 + b2 + c2 = (9)2 - 2 × 26
a2 + b2 + c2 = 29
a3 + b3 + c3 = (91 + 72 + 35)/2 = 99
From equation (1), by putting the values,
99 - 3abc = 9 × (29 - 26)
3abc = 72
abc = 24