Math Is Fun Forum

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.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

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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zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

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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.)