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if a,b,c are in A.P., prove that 8b^3-a^3-c^3=3ac(a+c)

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3 years ago

```							c-b=b-a2b=a+cb=(a+c)/2a^3+c^3-8b^3=a^3+c^3-8 ((a+c)/2)^3=a^3+c^3 - 8((a^3+3a^2c+3ac^2+c^3)/8)  (since (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3)=a^3+c^3-a^3-3a^2c-3ac^2-c^3=-3a^2c-3ac^2=-3ac(a+c) Or we can say 8b³-a³- c³ = 3ac(a+c)
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3 years ago
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