Challenge problem:

Given:

1) with

2) ,where are the roots of the above equation

Prove:

Moderator approved, CB

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- May 31st 2010, 02:49 PMalexandrosinequality
Challenge problem:

Given:

1) with

2) ,where are the roots of the above equation

Prove:

Moderator approved, CB - June 2nd 2010, 04:45 AMDefunkt
- June 2nd 2010, 07:26 AMalexandros
- June 7th 2010, 12:49 PMDefunkt
- June 7th 2010, 04:29 PMalexandros
- July 21st 2010, 08:30 AMmelese
Here is what I did.

By Vieta's formulas, we have , and . Then . And then, .

Now, we have , and since we arrive at (*) .

Eventually, . Notice that because .

It follows that ( is positive).

Also from (*), and it follows that .

From all this we get the inequality: . - July 21st 2010, 01:12 PMArchie Meade
There are a few typos in there...

(1)

Roots of f(x)=0 are

(2)

Prove the following...

**Proof**

or

Therefore

Hence...since

This is

it's already been established that

which is - July 25th 2010, 06:11 PMalexandros
Here is an easy double implication proof:

...................(since and )

............(since )