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

Asked by narayan_sanjeev | 9th Jul, 2019, 09:48: PM

Expert Answer:

If a+b+2c=0 , prove that a³+b³+8c³=6abc
 
We know that,
 
 
a3 + b + c - 3abc = (a + b + c)(a + b2 + c - ab - bc - ca)
 
If a + b + c = 0 → a3 + b + c = 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.

Answered by Yasmeen Khan | 10th Jul, 2019, 10:37: AM