Question

if a + b+ 2c =0 then find the value of a³+b³+8c³​

Answer 1

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 proveIf 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 prove