Hi. I had the problem below for homework. I think it is true, but I don't know why. Can anyone give me a reason why this is true, because I need to provide an explination. Thanks!

True or False:

If a<b then a3 <b3

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- September 9th 2009, 02:57 PMsleighHelp with True/False algebra inequality
Hi. I had the problem below for homework. I think it is true, but I don't know why. Can anyone give me a reason why this is true, because I need to provide an explination. Thanks!

True or False:

If a<b then a3 <b3

- September 9th 2009, 03:07 PM11rdc11
- September 9th 2009, 03:16 PMPlato
- September 9th 2009, 03:17 PMMatt Westwood
I assume you mean: if then .

It is actually true, but needs a fair amount of work to demonstrate.

First, you can show it's true when both and are positive, as follows.

You know that if then if then .

Okay, so implies (putting in the above).

Then implies (putting in the above).

So you've shown implies .

Do the same (similar) thing to prove for .

You go through a similar process when and are both negative, and again when is negative and positive.

An alternative approach makes use of the fact that the cube function is monotonically increasing - but that's really on a calculus course. - September 9th 2009, 04:57 PM11rdc11
- September 9th 2009, 08:56 PMMozart
- September 9th 2009, 11:09 PMMatt Westwood
- September 10th 2009, 12:48 AMLogic
I trust this works?

- September 10th 2009, 02:00 PMMatt Westwood
How sure are we that ?

- September 10th 2009, 05:11 PMKrizalid

Though you can't manipulate what you want to prove.