Missing one root
12-13-2020, 01:07 AM
Post: #1
 rrpalma Junior Member Posts: 29 Joined: Aug 2014
Missing one root
Hello,

I'm going over some simple math problems on both my HP50G and my Prime.

When I try to solve the very simple equation

(x-3)^(2/3) = 4

The HP50G correctly provides 11 and -5 as answers within a list

However the Prime only finds 11 as root, also within a list.

What gives?

12-13-2020, 01:38 AM
Post: #2
 Albert Chan Senior Member Posts: 1,996 Joined: Jul 2018
RE: Missing one root
Try using surd for the 1/3 power.

Cas> solve((surd(x-3,3)^2) = 4,x) ﻿ ﻿ ﻿ ﻿ ﻿ → {-5,11}
12-13-2020, 02:52 AM
Post: #3
 rrpalma Junior Member Posts: 29 Joined: Aug 2014
RE: Missing one root
(12-13-2020 01:38 AM)Albert Chan Wrote:  Try using surd for the 1/3 power.

Cas> solve((surd(x-3,3)^2) = 4,x) ﻿ ﻿ ﻿ ﻿ ﻿ → {-5,11}

Thanks!!! It worked.

However, I still would like to know what's behind the difference between how the 50G and the how the Prime find the roots.
12-13-2020, 03:45 AM (This post was last modified: 12-13-2020 03:56 AM by victorvbc.)
Post: #4
 victorvbc Member Posts: 71 Joined: Jun 2019
RE: Missing one root
(12-13-2020 02:52 AM)rrpalma Wrote:  Thanks!!! It worked.

However, I still would like to know what's behind the difference between how the 50G and the how the Prime find the roots.

By using the fractional exponent "1/3" the Prime returns the principal cube root, which in this case will be a complex number for any x<3. Whereas using surd or NTHROOT it returns the real-valued root instead, allowing for a zero at x=-5 in the equation (x-3)^(2/3)-4=0.

Edit: Wolfram Alpha for reference: https://www.wolframalpha.com/input/?i=%2...3%29-4%3D0

If you want to assume the real-valued root on the Prime, always use the root template key, nthroot, or equivalent.
12-13-2020, 04:33 AM
Post: #5
 rrpalma Junior Member Posts: 29 Joined: Aug 2014
RE: Missing one root
(12-13-2020 03:45 AM)victorvbc Wrote:
(12-13-2020 02:52 AM)rrpalma Wrote:  Thanks!!! It worked.

However, I still would like to know what's behind the difference between how the 50G and the how the Prime find the roots.

By using the fractional exponent "1/3" the Prime returns the principal cube root, which in this case will be a complex number for any x<3. Whereas using surd or NTHROOT it returns the real-valued root instead, allowing for a zero at x=-5 in the equation (x-3)^(2/3)-4=0.

Edit: Wolfram Alpha for reference: https://www.wolframalpha.com/input/?i=%2...3%29-4%3D0

If you want to assume the real-valued root on the Prime, always use the root template key, nthroot, or equivalent.

Thanks. Very much appreciated. I tried it both with NTHROOT and the template, and it worked. I'm still confused on why HP50G directly provides the real-valued root(s) whereas the Prime doesn't. I guess that's the way it is, and that's it. Or, how do I force then the HP50G to provide only the principal root?
12-16-2020, 02:12 AM (This post was last modified: 12-16-2020 02:20 AM by cdmackay.)
Post: #6
 cdmackay Senior Member Posts: 651 Joined: Sep 2018
RE: Missing one root
(12-13-2020 04:33 AM)rrpalma Wrote:  Or, how do I force then the HP50G to provide only the principal root?

I had thought that setting system flag -1 "principal value" might do it; but no, not with SOLVE.

Whereas if you use ISOL (isolate), it does honour the flag, but shows X=-5 only

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12-16-2020, 03:37 AM
Post: #7
 rrpalma Junior Member Posts: 29 Joined: Aug 2014
RE: Missing one root
(12-16-2020 02:12 AM)cdmackay Wrote:
(12-13-2020 04:33 AM)rrpalma Wrote:  Or, how do I force then the HP50G to provide only the principal root?

I had thought that setting system flag -1 "principal value" might do it; but no, not with SOLVE.

Whereas if you use ISOL (isolate), it does honour the flag, but shows X=-5 only

Thanks!! That's really odd :-)
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