Question

if a+b+c=9 and ab+bc+ca=26 then find the value of a^3+b^3+c^3-3abc

Answer 1

a+b+c = 9

Squaring on both sides.

(a+b+c)² = 9²

a²+b²+c²+2(ab+bc+ca)= 81

a² + b² + c² +2 (26) = 81.

a² + b² + c² + 52 = 81.

a² + b² + c² = 81-52

a² + b² + c² = 29


WE KNOW THAT

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

= [a+b+c] [a²+b²+c²- ( ab+bc+ca)]

= 9 [ 29 - 26 ]

= 9 [ 3]

= 27.

:)

Answer 2

Answer:

Hence the value of a 3 + b 3 + c 3 - 3 a b c is 27.