Math Is Fun Forum

aleclarsen12

Member

Registered: 2008-06-01

Posts: 36

Exact Solutions

It is evident by limits of the left and the right that there is only 3 real solutions for Q. Some guess and check shows that

but the third value is irrational. It is possible to approximate it however I want an exact solution. How can I find it?

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Exact Solutions

Hi aleclarsen12;

If you want the root closest to 0 it is.

To 50 digits.

I have been unable to find a closed form for that root. It may have one that I am overlooking but generally most numbers do not have nice representations like π / 2.

There are also other roots besides 0,1 and that .0915...

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.