New user with a question

[Xanthos]

Hey everyone,

New user here, so pardon my lack of knowledge. I just received my HP prime and have been watching a lot of YouTube videos about its operation. I stumbled upon this video comparing two other calculators. Video In this video he uses the solve function on both calculators on the equation (x^2-2^x=0,x). I figured I'd try it in the HP. However, I get the error message unable to isolate x. I've tried all different kinds of solvers in the calculator, but I never get any results. Any advice would be appreciated. It's probably something silly that I'm not doing. Thanks in advance.

[Spybot]

Hello!
the error you get, maybe because x^2-2-x^2=0 is not actually an equation...
x^2-2-x^2=0 if my maths are still correct, it is equals to: -2. so you're are trying to solve a number.

[Xanthos]

Sorry I had the equation wrong, I edited it so it's now accurate. Although you still may be correct, I'm not sure.

[Tim Wessman]

Hello,

This is actually a very interesting equation. It also highlights one of the primary differences between the Prime and the nspire/classpad.

Solving an *exact* symbolic solution for this equation is actually very difficult and requires something called the product log function. Never heard of it? Not surprising. Seems like it was pretty much invented to handle this type of construction where you *can't* define it by simply rearranging things algebraically.

Since none of the calculators support this function however, they can't provide an exact, symbolic result. What the other calculators do then, is just silently begin approximately solving in the background. This is why you end up getting decimal numbers that are *close* to the real result instead of an exact solution like b+sqrt(a+c)/3 or something.

The Prime however will NOT just silently start doing this. You asked it (by using the exact "solve(x^2-2^x,x)" command - the one labeled 1 Solve in your toolbox menu) to generate an exact solution. It first informs you that you didn't provide it an equation, and tells you that it is solving for x^-2^x=0 instead. It can't do so, so it errors and explains why. ("unable to isolate x in ...") You can then change to the numerical solve command, "fsolve(x^2-2^x,x)" (the one labelled 5 Numerical Solve) and it will spit out the results and an explanation of what it was doing.

Which of these is better? Well, that really is a personal preference. However, a lot of people do hold the opinion that anything that stops people from treating the calculator as a "magic box" and helps you think about what you are doing - and more importantly *why* you are doing it - can do nothing but help in math understanding.

The Prime also has significantly more powerful and capable CAS (computer algebra system) compared with either the nspire or classpad. With every CAS you will be able to find an example where it doesn't perform as well as another, but they are huge groups of advanced functionality that only the Prime has included. The others simply don't even try to include it.

One other little tip here. When you have the solve() command up in your entry line, press the HELP button. You'll see some help for the solve command. If you press the "Other" button in the help screen, you will find some related or similar commands. The "Numerical Solve" appears there. You can then jump to the help for that and learn about it.

Neither of the other units have extensive help built into the calculator with a single button press away. :-)

[Xanthos]

Tim,

Thank you very much for your help. I tried fsolve before and received the explanation. I assumed this to be an error message and backed out. Using your advice, I continued through the explanation and got the exact answer as the other calculators.

I've used HP calculators in the past, and appreciate their advanced features. I'm just extremely rusty with certain math at the moment and getting used to a new device. Hopefully the forum doesn't mind a few obvious questions every once in a while. Thank you again, and looking forward to enjoying and learning more about the calculator.

[Spybot]

OK but this equation has 3 roots (and they're all real) how come fsolve() only shows one of them? ( -0.7666647) while the other two are: 2 and 4.

[Tim Wessman]

Are you providing an initial guess? With no guess I see all 3.

[Terje Vallestad]

(10-06-2015 09:13 PM)Tim Wessman Wrote:  Are you providing an initial guess? With no guess I see all 3.

I think you see all 3 solutions only when Angle Measure is set to Radians, if Degrees are set you need to input a range to get them all.

Cheers, Terje

[Tim Wessman]

Yup, that would be it.

[Spybot]

Yes,as you guys mentioned above... switching the angle mode to radians allows me see all three roots. well... I guess I just learned something new today about the Prime commands and settings. Thank you.

[Xanthos]

Well I'm glad my simple question can help others learn more about their calculator. After all, I think that's why most of us are here.

[Dirk.nl]

Can someone explain to me the difference between CAS radians and CAS degrees?
I was thinking that everything inside the Prime was calculated in radians and degrees only used for presentation.

[cyrille de brébisson]

Hello,

Pretty much all numerical calculations are done in radian, this is correct.
But some calculations do have some impact depending on the angle mode.
For example the symbolic integration of sin(x).

Cyrille

[Dirk.nl]

Hi Cyrille,
Thanks for your answer!
I was thinking about the solve example of this thread, radians 3 solution and degrees 1 solution ( without a guess), but okay, I think I understand it now.

[Tim Wessman]

(10-09-2015 03:01 PM)Dirk.nl Wrote:  I was thinking about the solve example of this thread, radians 3 solution and degrees 1 solution ( without a guess), but okay, I think I understand it now.

What is happening specifically there is that some "default" arguments are being used for fsolve since none is provided. Bernard has it so that the default will be a suitable range for trig functions with either degree, or rads.

[Dirk.nl]

Thanks Tim!