Question

If a+b+c=3, abc = (-12) and ab+bc+can = (-4) find the value of a^3+b^3+c^3

Answer 1

(a+ b + c) ³= a³+b³+c³+2(ab+bc+ca

Answer 2

Let a = x and (b +c) = y.

(x + y)³ = x³ + y³ + 3xy ( x + y)

Now substitute the values.

(a + b +c)³ = a³ + (b + c)³ + 3abc (a + b + c)

(a + b + c)³ = a³ + b³ + c³ + 3abc (a + b + c)

Now substitute the values given in the question.

(3)³ = a³ + b³ + c³ + 3 × -12 × -4

27 = a³ + b³ + c³ + 144

a³ + b³ + c³ = 27 - 144

= -117

Ans = -117

Hope it helps! ^^