If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 - 3abc = - 25

see explanation

Step-by-step explanation:

Using the identity

(a + b + c) ³ = a³ + b³ + c³ + 3 [ (a + b + c) (ab + bc + ac) - abc ], then

5³ = a³ + b³ + c³ + 3 (5 * 10) - 3abc, that is

125 = a³ + b³ + c³ + 150 - 3abc, hence

a³ + b³ + c³ - 3abc = 125 - 150 = - 25