# Math Help - Challenging riddle

1. ## Challenging riddle

I solved it and found it pretty challenging so I thought I could share it with you people. And please, if you already solved it beforehand or if you check on the Internet for the answer, don't ruin the fun. Thanks!

$\overline{AD} = 1cm$

$\overline{EC} = 0.5 cm$

$\overline{AD} = \overline{EB}$

Find $\overline{DB}$.

Spoiler:
$\sqrt[3]{2}$ or $2^{\frac{1}{3}}$

2. Hello,

3. Originally Posted by Moo
Hello,

Wouldn't it be too easy it AD=ED? One step and you would be done ...

It is as I stated, AD=EB.

4. Thank you. I enjoyed that puzzle - not hugely taxing but very satisfying nonetheless!

5. ## Quest.

Hope this isn't too much of a spoiler

How do I solve the resulting quartic equation to obtain the answer?

6. Spoiler:

Any polynomial whose coefficients are integers will, if it has an integer solution, have an integer solution that is a factor of the coefficient of the zeroth order term i.e. the constant. For example look at the general quartic:

$a x^4 + b x^3 + c x^2 + d x + e = 0$

where the coefficients $a$ through $e$ are integers. Well if there is an integer solution to this then it will be a factor of $e$. So look at that constant in your quartic and (assuming you have the right quartic) try each of it's factors to see if one is a solution. Then you can simply factor that solution out.

Have fun!

7. Originally Posted by the_doc
Spoiler:

Any polynomial whose coefficients are integers will, if it has an integer solution, have an integer solution that is a factor of the coefficient of the zeroth order term i.e. the constant. For example look at the general quartic:

$a x^4 + b x^3 + c x^2 + d x + e = 0$

where the coefficients $a$ through $e$ are integers. Well if there is an integer solution to this then it will be a factor of $e$. So look at that constant in your quartic and (assuming you have the right quartic) try each of it's factors to see if one is a solution. Then you can simply factor that solution out.

Have fun!
Spoiler:
$a^4 + 2a^3 - 2a - 4 = 0$ becomes $(a + 2)(a^3 - 2) = 0$. Step by step on how to solve a quartic equation is a shotgun ammo in someone's head, trust me. xD

I'll PM you the step by step guide though.