Question

If a2+b2+c2=13 and ab+bc+ca=6 then evaluate a3+b3+c3-3abc

Answer 1

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac 
(a + b + c)² = 13 + 2(6) 
(a + b + c)² = 25 
a + b + c = 5 or -5 

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

when (a + b + c = 5), 
a³ + b³ + c³ - 3abc 
= (5)(13 - 6) 
= (5)(7) 
= 35 
when (a + b + c = -5), 
a³ + b³ + c³ - 3abc 
= (-5)(13 - 6) 
= (-5)(7) 
= -35 

Answer 2

(a+b+c)=root of (a²+b²+c²+2(ab+bc+ac))=root of(13+2*6)=root Of (13+12)=root of 25=5 or -5

a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
=(a+b+c)(a²+b²+c²-(ab+bc+ac))
case 1 whena+b+c=5, =>5*(13-6)=5*7=35
case 2 when a+b+c=-5
=>-5*(13-6)=-5*7=-35

hope it is not wrong and helps you