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+--- Thread: Missing one root (/thread-16046.html)
Missing one root - rrpalma - 12-13-2020 01:07 AM
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?
Thanks for reading.
RE: Missing one root - Albert Chan - 12-13-2020 01:38 AM
Try using surd for the 1/3 power.
Cas> solve((surd(x-3,3)^2) = 4,x) → {-5,11}
RE: Missing one root - rrpalma - 12-13-2020 02:52 AM
(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.
RE: Missing one root - victorvbc - 12-13-2020 03:45 AM
(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=%28x-3%29%5E%282%2F3%29-4%3D0
If you want to assume the real-valued root on the Prime, always use the root template key, nthroot, or equivalent.
RE: Missing one root - rrpalma - 12-13-2020 04:33 AM
(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=%28x-3%29%5E%282%2F3%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?
RE: Missing one root - cdmackay - 12-16-2020 02:12 AM
(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
RE: Missing one root - rrpalma - 12-16-2020 03:37 AM
(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 :-)