Question

a+b+c =8
a ² + b ² + c^2=34 then a3+b3+c3-3abc=??​

Answer 1

$\bf\large\underline\pink{Solution :-}$

Given,

a + b + c = 9 ...(i)

a² + b² + c² = 35 ...(ii)

➽ (a + b + c)² - 2 (ab + bc + ca) = 35

➽ 9² - 2 (ab + bc + ca) = 35

➽ 2 (ab + bc + ca) = 81 - 35

➽ 2 (ab + bc + ca) = 46

➽ ab + bc + ca = 23 ...(iii)

Now,

a³ + b³ + c³ - 3abc

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

= (a + b + c) {(a² + b² + c²) - (ab + bc + ca)}

= 9 (35 - 23), using (i), (ii) and (iii)

= 9 × 12

= 108

Answer 2

Answer:

a3+b3+c3-3abc=152 , ab+bc+ca=15