Melody

Multiply both sides by 15.

Great!

Research papers DO sound a LOT less interesting than maths!  

3x + x√3 = 3 + 3√3

$$x(3+\sqrt3)=3(1+\sqrt3)\\\\
x=\frac{3(1+\sqrt3)}{(3+\sqrt3)}\\\\
x=\frac{3(1+\sqrt3)}{(3+\sqrt3)}\times \frac{(3-\sqrt3)}{(3-\sqrt3)}\\\\
x=\frac{3(3+2\sqrt3-3)}{(9-3)}\\\\
x=\frac{3(2\sqrt3)}{6}\\\\
x=\sqrt3\\\\$$

How about that!

Tues 140506

Thank you

Why don't you sign up and become a permanent recognised part of our community?

So are the numbers the relative areas?

It is interesting that you can upload even though you are not a member.  That is new.

I will include this post in my 

"End of Day Wrap" tonight.  I find it interesting and I think other people will too.

Thanks you.

I like getting a few clean jokes onto the forum.  Thank you

Can you show us a picture of this fibonacci spiral please.  I don't know what you mean and I am interested.

Do you know how to upload a picture.  If you are not a member then i don't think you can anyway.

Maybe you could just paste a web address in for us.

Have you tried googling it?  

For general questions like this it is often better to google the question first and then come here if you can't find what you are after.

I am just trying to be helpful.

$$x^2-8$$

arc cos is the same as inverse cos

$$acos(ratio)=cos^{-1}(ratio)$$

If you have done a little trigonometry you will know what I mean.