# Thread: I am a banana. Or an ENTP. Whichever.

1. ohhh, banana... you must write like a million times faster than the average person or something to be able to unleash your dribble like that. You better post heaps here, I think we need more ENTPs with your style around. Are you a mathematician?

Can you solve this, rationalize and simplify:
((4 + h)^0.5 - 2)/h

2. Yes I type fast, somewheres between 80-100wps usually, more or less, depends on how much I have to think on it, and whether I get stuck thinking of the right word or not. Happens alot really.

As for the mathematician, I used to be strong in maths, but got bored of them, more interested in the theory than the practice part of it honestly XD

For the answer to the question though, I'm working on it... been a long time since I've had to do this kind of problem. The square root exponent isn't so much the problem, as the annoying variables and lack of anything consistant in the problem is.

Still, lemme see...

((4 + h)^0.5 - 2)/h

(4+h)^0.5 -2 = h
4+h -2^2 = h^2
h=h^2 <-- at this point it basically is either h=1 or h=0 being the only two possibilities...
h^0.5 = h
(1h)^0.5 = 1h
1^0.5 = 1 <-- is this step even allowed? O.o
1 = 1^2
1 = 1

I have nooooooooo clue how accurate that is and I'm relatively sure I screwed something up somewhere, but I'm really not sure. It's been aaaaaaages since I've had to play with that kind of maths sadly.

But it came out to a whole number in the end so I'm going to hope that's right XD

EDIT!

DURR! I just realized after posting that I screwed something up that should've saved me a few steps XD

h=h^2
h/h = (h^2)/h
1 = 1^2
1 = 1

Same answer but that makes more sense somehow.

(To give an idea of how long it's been, I had to doublecheck on the definitions of solve, rationalize and simplify...)

3. I kinda preferred banana but as long as you are full of potassium I welcome you with open arms to the forum.

4. And people say I talk alot...

5. Originally Posted by Katsuni
Yes I type fast, somewheres between 80-100wps usually, more or less, depends on how much I have to think on it, and whether I get stuck thinking of the right word or not. Happens alot really.
:O ... ummm... Okay... my competence has now been questioned and I'm going to spend the next 5 days trying to type 5 times as fast as I do now

As for the mathematician, I used to be strong in maths, but got bored of them, more interested in the theory than the practice part of it honestly XD

For the answer to the question though, I'm working on it... been a long time since I've had to do this kind of problem. The square root exponent isn't so much the problem, as the annoying variables and lack of anything consistant in the problem is.

Still, lemme see...

((4 + h)^0.5 - 2)/h

(4+h)^0.5 -2 = h
4+h -2^2 = h^2
h=h^2 <-- at this point it basically is either h=1 or h=0 being the only two possibilities...
h^0.5 = h
(1h)^0.5 = 1h
1^0.5 = 1 <-- is this step even allowed? O.o
1 = 1^2
1 = 1

I have nooooooooo clue how accurate that is and I'm relatively sure I screwed something up somewhere, but I'm really not sure. It's been aaaaaaages since I've had to play with that kind of maths sadly.

But it came out to a whole number in the end so I'm going to hope that's right XD

EDIT!

DURR! I just realized after posting that I screwed something up that should've saved me a few steps XD

h=h^2
h/h = (h^2)/h
1 = 1^2
1 = 1

Same answer but that makes more sense somehow.

(To give an idea of how long it's been, I had to doublecheck on the definitions of solve, rationalize and simplify...)
I found this question in a diagnostics test for calculus and I've been thinking about it for a little while and I can't solve it, I have the answer, and still it makes no sense at all. To rationalize usually means to rationalize the denominator (eg. change 5/sqrt2 to (5*sqrt2)/2). To simplify is to put into a usable form, it's rather subjective, so more than one answer may be right. To solve is to find the answer to the question -_-' (lol).

The problem with your solution:
1. You can't actually bring an equals sign in like that, unless they tell you that the equation equals, well in this case, one.

Well, the answer is 1/((h+4)^0.5)+2), and it looks like they've rationalized the numerator. I can't do it... I've asked the citizens of Facebook to no avail, so it must be time to find Captain Nemo in the maths thread.

6. Actually I originally did it using n for the equals, so if yeu go back and do it this way...

((4 + h)^0.5 - 2)/h = n (which we know to be true due to being a variable itself, n represents whotever it actually ends up being)

(4+h)^0.5 -2 = nh
4+h -2^2 = (nh)^2
h=(nh)^2
h^0.5 = (nh)
(1h)^0.5 = n1h <--- it's a multiplication so the order doesn't matter, can just break it this way to make more sense
1^0.5 = n1
1 = n1^2
1 = n1
Therefore...
1/1 = n
And 1 = n

So I actually did use the = sign correctly I just forgot to write in the variable I was using sorry >.>;

7. Originally Posted by Katsuni
Actually I originally did it using n for the equals, so if yeu go back and do it this way...

((4 + h)^0.5 - 2)/h = n (which we know to be true due to being a variable itself, n represents whotever it actually ends up being)

(4+h)^0.5 -2 = nh
4+h -2^2 = (nh)^2
h=(nh)^2
h^0.5 = (nh)
(1h)^0.5 = n1h <--- it's a multiplication so the order doesn't matter, can just break it this way to make more sense
1^0.5 = n1
1 = n1^2
1 = n1
Therefore...
1/1 = n
And 1 = n

So I actually did use the = sign correctly I just forgot to write in the variable I was using sorry >.>;
Okay, I asked the maths thread, and Liquid Laser said to just multiply the whole thing by ((4+h)^.5 +2) / ((4+h)^0.5 +2), you can add this because it equals 1, and multiplying anything by one will not change the answer. The entire top line becomes 4 + h - 4 (difference of squares- square the first term, subtract the square of the second term), then the fours cancel, leaving you with h, and that cancels with the h on the bottom, leaving you with 1/ ((4+h)^0.5 + 2). That's how ye doooo it!!!
___________________________________________
Unfortunately, your n thing doesn't work either, if you have h^0.5=hn, then it will become n = h^-0.5

which can then be substituted back into the original:
(4+h)^0.5 -2 = h^-0.5 * h

(4+h)^0.5 -2 = h^0.5

((4 + h)/h)^0.5 - 2/(h^0.5) = 1

((4 + h)/h) - ((16 + 4h)/(h^3/2)) - 4/h = 1

4h + h^2 - 16(h^0.5) + 4(h^3/2) -4h = h^2

4(h^3/2) - 16(h^0.5) = 0

h^2 - 4h = 0

h^2 = 4h

h = 4

n= 0.5

hmmm, I think I might have forgot to include a negative somewhere, and that's not really what the question asked, it still surprisingly enough managed to get somewhere eventually

8. Alright I'll concede that then XD

One thing does bother me though... this line in the reiteration of it:

(4+h)^0.5 -2 = h^-0.5 * h

(4+h)^0.5 -2 = h^0.5

So uhm.. the extra h just... disappeared to nowheres? O.o; As we haven't proven h = 1 as of yet, that can't be done :o

But still, the above explaination makes alot more sense, I figured it'd be something stupidly easy since I KNOW I spent a whole night for several hours working through problems like this once years ago, and they all were supposed to be really easy with a simple way to do them by cross multiplication and canceling out... which I didn't know so I did each one slowly in the traditional way... which took forever and made a mess of a few of them >.>

Oh well XD

At least now I remember how to do it now that I've been shown again, and understand why it works!

And now I'll never use it again. Ever.

9. Welcome

10. Hi banana

I dont know whats going on but I've just seen this and it doesnt look right :

((4 + h)^0.5 - 2)/h

(4+h)^0.5 -2 = h

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