# How is this possible?

1. Jan 19, 2008

### danni7070

$$\sqrt{e^{2t}+2+e^{-2t}} = e^t+e^{-t}$$

I just can't see it.

2. Jan 19, 2008

### neutrino

The square root of expression A is expression B. So, what is the square of expression B?

3. Jan 19, 2008

### rocomath

$$\sqrt{e^{2t}+2+\frac{1}{e^{2t}}}$$

Simplify it, then put it in the sum of a product form.

4. Jan 19, 2008

### danni7070

$$(e^t+e^{-t})^2 = e^{2t}+2+e^{-2t}$$

Not 100% sure but is e^t+e^-t = 1 ?

5. Jan 19, 2008

### rocomath

No but ... this is equal to 1

$$\frac{e^t}{e^t}=1$$

6. Jan 19, 2008

### danni7070

sorry I meant e^t * e^-t = 1

because e^t * 1/e^t = 1....

7. Jan 19, 2008

### arildno

No it is not, don't mix * with +!

8. Jan 19, 2008

### ghost02

I know this is a stupid question, but is there a website that shows what the letters after the exponents stand for?

9. Jan 19, 2008

### rocomath

I'm not sure what you're asking :(

10. Jan 19, 2008

### HallsofIvy

Staff Emeritus
Is there a webset that shows what the letter "x" stands for? You can let letters stand for whatever you want. Perhaps it would make sense if gave an example to show exactly what you mean.

11. Jan 19, 2008

### ghost02

like [Tex] e^{2t} [/Tex] what would the t stand for?

12. Jan 19, 2008

### rocomath

$$e^t$$ ???

t can be any number, it could even be $$x^2$$

$$e^3$$

or

$$e^{x^2}$$

In general, the letters at the beginning of the alphabet are denoted for constants such as numbers 1, 2, 3 ... etc. while the letters at the end of the alphabet ... x, y, z are used for variables ... an unknown number that we're looking for.

Last edited: Jan 19, 2008
13. Jan 20, 2008

### ghost02

Ahh ok. Thank you very much. I thought it meant specific numbers!

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