Question

if a+b+c=9,ab+bc+ca=26,then find the value of a3+b3+c3-3abc

Answer 1

a+b+c=9,ab+bc+ca=26

⇒ a² + b² + c² = (a + b + c)² - 2(ab + bc + ca)

= 9² - 2(26)

= 81 - 52

= 29



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

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

= 9 (29 - 26)

= 9 (3)

= 27

Hope it helps