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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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closed as off-topic by JMP, boboquack, Oray, Jaap Scherphuis, Jamal Senjaya Jan 20 '18 at 11:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – boboquack, Oray, Jaap Scherphuis, Jamal Senjaya
If this question can be reworded to fit the rules in the help center, please edit the question.

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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 Jan 21 '18 at 1:37
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    $\begingroup$ @Jasen are you assuming DC is parallel to the bottom segment? $\endgroup$ – boboquack Jan 22 '18 at 23:54
  • $\begingroup$ @boboquack Yes. I was. Oops! $\endgroup$ – Jasen Jan 23 '18 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 Jan 23 '18 at 5:33

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