Question

If a+b+c=0,show that a^3+b^3+c^3=3abc​

Answer 1

Answer:

in ncert book of ninth class, PG-48

identity 8

if x'3+y'3+z'3 - 3xyz= 0 (x'2 + y'2 + z'2 - xy - yz - xz) (x+y+z=0)

x'3+y'3+z'3 - 3xyz = 0

then,

x'3 + y'3 + z'3 = 3xyz

x=a

y=b

z=c

Answer 2

Answer:

We know that ,

• a^3+b^3+c^3-3abc=(a+b+c) (a^2+b^2+c^2-ab-bc-ca) .... (1)

we are given that (a+b+c) =0....... (2)

comparing (1) and (2),

we get

a^3+b^3+c^3-3abc=(0) (a^2+b^2+c^2-ab-bc-ca)

which results in a^3+b^3+c^3-3abc=0

that's a^3+b^3+c^3=3abc

Hence Proved//