Why isn't it B cubed?

Algebra Level 4

1a4+1b4+1c4=1\dfrac{1}{a^4}+\dfrac{1}{b^4}+\dfrac{1}{c^4}=1

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

Find the minimum value of

a4b4+a4c4+b4c4a3b2c3\dfrac{a^4b^4+a^4c^4+b^4c^4}{a^3b^2c^3}

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

This is part of the set Trevor's Ten

Details and Assumptions

  • The answer is not 300300.

  • It is indeed a3b2c3a^3 b^2 c^3 and not a3b3c3a^3 b^3 c^3

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