Question

if(a+b+c)=0 prove not a cube + b cube+8 c cube= 6 abc​

Answer 1

Question:-

if(a+b+c)=0 prove not a cube + b cube+8 c cube= 6 abc​

To prove:-

a cube + b cube+8 c cube= 6 abc​

Answer:-

Step-by-step explanation:-

If a+b+2c=0 , prove that a³+b³+8c³=6abc  

We know that,  

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

If a + b + c = 0 → a3 + b3  + c3  = 3abc   ... (i)  

L.H.S = a³+b³+8c³

        = a³+b³+(2c)³  

It is given that  a+ b + 2c = 0.

→ a³+b³+(2c)³ = 3ab(2c)       .... from (i)

→ a³+b³+(2c)³ = 6abc = R.H.S

 

Hence proved.