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If a,b and c are in A.P A 2 +c 2 +4ac=2(ab+bc+ac). How to prove it .... a^3+b^3+6abc = 8b^3

If a,b and c are in A.P
A2+c2+4ac=2(ab+bc+ac). How to prove it ....
a^3+b^3+6abc = 8b^3
 

Grade:11

1 Answers

Kunal Singh
36 Points
7 years ago
WE know that since a,b, c are in A.P
therefore a+c/2=b
              a+c=2b
2(ab+bc+ac) can be written as 2ab+2bc+2ac
=2b(a+c)+2ac
=(a+c)(a+c)+2ac
=(a+c)^2+2ac
=a^2 +c^2+2ac +2ac
=a^2+c^2+4ac..
Hence proved
 

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