Question

If a+b+c=5, a² +b² +c² =27,
a ^3+ b^3 + c^3 = 125 then 4abc?​

Answer 1

(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)

5^2 = 27 + 2(ab + bc + ca)

25 = 27 + 2( ab + bc + ca)

2(ab + bc + ca ) = 25 - 27 = -2

ab + bc + ca = -1

now

a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)

125 - 3abc = 5 (27 - (-1))

125 - 3abc = 5 (27 + 1)

125 - 3abc = 5*28

125 - 3abc = 140

-3abc = 140 - 125 = 15

abc = 15/-3 = -5

now,

4abc = 4*(-5) = -20