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Considering it's the beginning of a new year, I have created the following challenge. I hope to make one every month until December 2018!

Here goes:

enter image description here

Show that $AD-AB>AC^3$. Do not use scale drawings.

Note that this post was advised to be migrated to Puzzling Stack Exchange from Mathematics.

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    $\begingroup$ the diagram given seems sufficient to give precise lengths for every line segment, so the lengths can be resolved to surds and the inequality proven that way, $\endgroup$
    – Jasen
    Commented Jan 21, 2018 at 1:37
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    $\begingroup$ @Jasen are you assuming DC is parallel to the bottom segment? $\endgroup$
    – boboquack
    Commented Jan 22, 2018 at 23:54
  • $\begingroup$ @boboquack Yes. I was. Oops! $\endgroup$
    – Jasen
    Commented Jan 23, 2018 at 5:26
  • $\begingroup$ @boboquack but if it's not disproof is trivial. it sure looks like AD−AB can be made negative. $\endgroup$
    – Jasen
    Commented Jan 23, 2018 at 5:33

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