Can someone help me to solve this equation?

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- January 9th 2006, 05:32 PMDenMac21Equation help
Can someone help me to solve this equation?

- January 9th 2006, 07:08 PMThePerfectHackerQuote:

Originally Posted by**DenMac21**

Thus,

Now notice that,

Thus,

Further, factor thus,

.

But I did not finish it, I do not know if that helps.

Thus, one solution is - January 9th 2006, 07:43 PMDenMac21Quote:

Originally Posted by**ThePerfectHacker**

- January 10th 2006, 08:57 AMDenMac21Help - equation
Can someone help me to solve this equation?

- January 10th 2006, 10:19 AMticbolQuote:

Originally Posted by**DenMac21**

x^4 -2ax^2 +a^2 = a -x

(x^2 -a)^2 = a-x

x^2 -a = +,-sqrt(a-x) ----------(1)

The RHS +,-sqrt(a-x):

----"a" cannot be zero because sqrt(-x) is not real.

----"a" cannot be negative because the radicand will be negative.

So, a > 0 ----------(i)

Then,

----for (a-x) to be positive, x < a -----------(ii)

----since "a" cannot be negative and x<a, then x cannot be negative too.

In the whole (1):

---x cannot be zero because (-a) cannot be equal to +,-sqrt(a).

Hence, x > 0

Therefore, 0 < x < a, but x cannot be zero. --------answer. - January 10th 2006, 10:24 AMTD!
I don't really understand a lot of your answer...

"*----"a" cannot be zero because sqrt(-x) is not real.*"?

And what if x is negative? Then surely sqrt(-x) exists, no? It's not specified that x is a positive number, I think it's just a real number... - January 10th 2006, 10:27 AMticbolQuote:

Originally Posted by**TD!**

- January 10th 2006, 10:41 AMThePerfectHacker
Ha ha, I missed that, you are right.

Try this,

Thus,

But for the second factor I did not solve it.

I do not know if this helps. - January 10th 2006, 10:44 AMTD!
The step from line 4 to line 5 isn't correct, x = a isn't a solution which can be easily verified.

- January 10th 2006, 10:50 AMThePerfectHackerQuote:

Originally Posted by**TD!**

- January 10th 2006, 10:52 AMTD!Quote:

Originally Posted by**ThePerfectHacker**

- January 10th 2006, 10:55 AMticbolRe TD! comment on my answer.Quote:

Originally Posted by**ticbol**

I have to go to work now to put some food on the table. I will be back in about 12 hours from now. Maybe by then you could show us why you think x could be negative. Then I would comment on your posting.

ticbol

-----------

Like I said before somewhere in this Forum, I do not comment on somebody's answer whether that answer is correct, wrong, lacking, too long, whatever.

But, of course, I will comment on any comment re my answers. - January 10th 2006, 10:55 AMThePerfectHacker
DenMac21 do not make double threads on the same topic please.

As I am looking on the equation I do not see any basic way of doing it do you TD!? There is definetly a solution to it by the fundamental theorem. - January 10th 2006, 11:02 AMTD!
I haven't really looked into the problem so I haven't been able to come up with a more elegant solution, but here's a go.

We have a 4th degree polynomial without a 3rd degree term so a possible factorization would be two second degree polynomials with opposite lineair terms.

Identifying coefficients gives us a 3x3 system

Solving yields

So we have the following factorization

Then it's just solving two quadratics, solutions are

Of course, these solutions for x depend on a, so I don't see why a negative solution would be impossible - for certain values of the parameter a. - January 10th 2006, 11:17 AMThePerfectHacker
You can always use the quadtric formula!!! :D