Why isn't it B cubed?

Algebra Level 5

$\dfrac{1}{a^4}+\dfrac{1}{b^4}+\dfrac{1}{c^4}=1$

Given the above equation for positive numbers $$a,b,c$$.

Find the minimum value of

$\dfrac{a^4b^4+a^4c^4+b^4c^4}{a^3b^2c^3}$

If the minimum value of the above is $$x$$, input your answer as $$\lfloor 100x \rfloor$$.

This is part of the set Trevor's Ten

Details and Assumptions

• The answer is not $$300$$.

• It is indeed $$a^3 b^2 c^3$$ and not $$a^3 b^3 c^3$$

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