Melody

$${\frac{{\mathtt{100\,000}}}{{\mathtt{1.072}}}} = {\mathtt{93\,283.582\: \!089\: \!552\: \!238\: \!806}}$$

Welcome to the forum garanceme.  I hope that you like it here.

It is great to see you answering a question.  (I gave you the thumbs up and the 3 point)

If you are answering a question like this you can just use the 'math(input=Result)' Button.

It is easier than reaching for a different calc and it displays the working.  

I think that is the same as

$$(2x+x\sqrt3)(2x+x\sqrt3-2x)^2(2x+x\sqrt3-2x\sqrt3)=144\sqrt3\\

Do you agree?\\

(2x+x\sqrt3)(x\sqrt3)^2(2x-x\sqrt3)=144\sqrt3\\


3x^2((2x)^2-(x\sqrt3)^2)=144\sqrt3\\

3x^2(4x^2-3x^2)=144\sqrt3\\\\

3x^2(x^2)=144\sqrt3\\\\

3x^4=144\sqrt3\\\\

x^4=\frac{144\sqrt3}{3}\\\\

x=\pm\left(\frac{144\sqrt3}{3}\right)^{(1/4)}\\\\$$

$${\left({\frac{{\mathtt{144}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}}{{\mathtt{3}}}}\right)}^{{\mathtt{0.25}}} = {\mathtt{3.019\: \!607\: \!296\: \!954\: \!21}}$$

I did this on the site calc

x ≈ ± 3.019607

That's assuming I didn't make any stupid mistakes.

Now you can either tell me I am wrong or you can say thank you!  

Yes - Good one David  

Hi Bioschip, DavidQD and anonymous,

I have seen commas used as decimal points (this is quite common - I think my students that used to do it were from African nations, maybe Sierra Leone? Not sure) but I have never seen periods (dots) used to separate place value!   

Which countries do that ?  Maybe DavidQD or our anonymous person could tell me?

(((2x+x*sqrt(3))/2))(((2x+x*sqrt(3))/2-x)((2x+x*sqrt(3))/2-x))*((2x+x*sqrt(3))/2-x*sqrt(3)))=9*sqrt(3)

First I want to make sense of it!

Is this your question?

$$\left(\frac{(2x+x\sqrt3)}{2}\right)\left(\frac{(2x+x\sqrt3)}{2}-x\right)\left(\frac{(2x+x\sqrt3)}{2}-x\right)\left(\frac{(2x+x\sqrt3)}{2}-x\sqrt3\right)=9\sqrt3$$

It's too long - it won't display on one line!

Hi Bioschip,

I really like your logic there.  And of course you are correct.  6 IS ONE of the answers !   

When you have an equation like this with an x² term, there are usually 2 answers.

this is how it is done.   

$$x^2-2x-24=0$$ 

First I need to factorise this.  Factors are things that multiply to get the answers

I need 2 numbers that multiply to -24  (one will need to be neg and one pos)

they also need to add to -2   (How about -6 and 4, they work)

so the question becomes

$$(x-6)(x+4)=0$$      that is what Bertie got up to!

NOW, if two things multiply together to give 0 then one of them (or both of them) must equal 0.

so either $$x-6=0$$  or  $$x+4=0$$

so   $$x=6$$   OR    $$x=-4$$  

Maybe you would like to try this one   $$x^2+5x+4=0$$   ???

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NOW I want people to start learning to use LaTex which is how we display the maths stuff.

So here is a little lesson.

Press the LaTex button, type (x-6)(x+4)=0  then press ok.

See how it displays.  

If you want to know how to display anything else, please ask.  Remember, Members get priority answering.  

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Help you with what????

Thanks Mathwizard, it didn't occur to me that it was a minus sign, I just thought it was a dash!

$$\sqrt{-4\; }$$  has no solution in the real number system because nothing multiplied by itself equals a negative number.

--------------------------

University people will tell you that  $$\sqrt{-1}= i$$  This is the base unit for all imaginary numbers.

so we could say that $$\sqrt{-4}=\sqrt{-1}\times\sqrt4 = i\times2=2i$$

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I think it would  be good if people started to learn LaTex.  That is what I used to write that maths stuff.

This is how to write sqrt of 4

click on the LaTex Formula button in the tool bar

enter \sqrt4  then press ok

It is that simple, if you want square root of 16 this is what you must enter

\sqrt{16}  then ok

If you didn't put the curly brackets then only the 1 would be under the sqare root sign.  

why don't you give it a go - if you would like to know how to write something else just ask.  

Hang on a moment, I don't think that the question was finished. Surely there was supposed to be an equal sign and another number at the end?????

Still, what you have both said is right of course.

Hi Mathwizzard91472  it is great to see you answering this question.  It was a really good answer too. 

8pi/2 is 2 complete revolutions so 11pi/2 is the same as 3pi/2 as far as the value of sine is concerned.

On the unit circle, 3pi/2 is the point (0,-1)  DRAW it do see what i mean.

sine is given by the y value on the unit circle so sin(3pi/2)= -1

So

sin(11pi/2)= -1

I can try and explain more, maybe with a diagram, if you need me too.