# True or false or it depends?

Algebra Level 3

True or false:

If $$a\left(\dfrac{1}{b} + \dfrac{1}{c}\right) , b\left(\dfrac{1}{c} + \dfrac{1}{a}\right) , c\left(\dfrac{1}{a} + \dfrac{1}{b}\right)$$ are in arithmetic progression where $$a,b,c$$ are real numbers not equal to 0 then $$a^3 + c^3 + 6abc$$ equal to $$8b^3$$.

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