Discover the Surprising Simplification of \sqrt{e^{2t}+2+e^{-2t}}

[danni7070]

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

I just can't see it.

 

[neutrino]

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

 

[rocomath]

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

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

 

[danni7070]

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

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

 

[rocomath]

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

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

No but ... this is equal to 1

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

 

[danni7070]

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

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

 

[arildno]

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

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

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

 

[ghost02]

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

 

[rocomath]

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

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

 

[HallsofIvy]

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

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.

 

[ghost02]

like $$e^{2t}$$ what would the t stand for?

 

[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.

 

[ghost02]

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