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#1 2021-12-27 02:14:33

nahid
Member
Registered: 2021-12-27
Posts: 1

How can I prove this equation

Hi, I have math which is really confusing to me. Any kind of help will be appreciated.

Math image

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#2 2021-12-28 03:14:08

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,199

Re: How can I prove this equation

I know this probably isn't the intended way of solving it, but you could just solve the quartic with some simple completing the square, and hence prove the expression on the right.


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#3 2021-12-28 04:11:45

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,376
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Re: How can I prove this equation

Hi nahid,

Welcome to the forum.

Are you sure you've posted the problem correctly? As it stands, I can't see how the latter statement is true. We have:

and so

since obviously
But then the problem statement suggests that we should then have
whereas the polynomial
doesn't have any real roots. (You can show this by differentiating it once to find the stationary point, then again to show that it's a minimum -- then showing that at this minimum,
is strictly positive, i.e. doesn't ever cut the x-axis.)

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