Question

if a +b+c =6, ab+bc+ca=-1 and abc=-30 then find the value of a³+b³+c³= ​

Answer 1

Step-by-step explanation:

given a+b+c = 6 , ab + bc + ca = 11

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

⇒ (6)² = a² + b² + c² + 2(11) ⇒ a² + b² + c² = 36-22 = 14

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

⇒ (6)(14 - 11) = 6. 3 = 18