ICSE Class 9 Answered
If a+b+2c=0 , prove that a³+b³+8c³=6abc
Asked by narayan_sanjeev | 09 Jul, 2019, 09:48: PM
Expert Answer
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.
Answered by Yasmeen Khan | 10 Jul, 2019, 10:37: AM
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