Question

If a+b+c=14, a2+b2+c2=74 and a3+b3+c3=434 find abc​

Answer 1

Answer:

84 is the answer.

Solution

We know, (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) => (14)2 = 74 + 2(ab + bc + ca) => ab + bc + ca = 122 / 2 = 61

Again, using a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)

434 - 3abc = 14 (74 - 61)

434 - 3abc = 14 (13)

434 - 3abc = 182

3abc = 434 - 182 = 252

Abc = 252/3 = 84 (Answer)