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+--- Thread: Fireworks while trying to solve system of equations (/thread-17198.html)
Fireworks while trying to solve system of equations - dah145 - 07-02-2021 05:22 PM
Trying to solve this system of non linear equations makes my HP Prime display some nice fireworks:
solve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z])
It also crashes the virtual calculator on PC.
RE: Fireworks while trying to solve system of equations - Albert Chan - 07-03-2021 12:35 AM
Quote:solve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z])
This crash on XCas as well.
We can simplify system of equations into 1 equation.
For real solutions, equating y:
CAS> z := sqrt(exp(sqrt(x))/3)
CAS> fsolve(sqrt(z^3/x) = (5*z*x)^(1/x), x)
[0.281669416538, 11.005909666]
RE: Fireworks while trying to solve system of equations - dah145 - 07-03-2021 07:20 PM
(07-03-2021 12:35 AM)Albert Chan Wrote:Quote:solve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z])
This crash on XCas as well.
We can simplify system of equations into 1 equation.
For real solutions, equating y:
CAS> z := sqrt(exp(sqrt(x))/3)
CAS> fsolve(sqrt(z^3/x) = (5*z*x)^(1/x), x)
[0.281669416538, 11.005909666]
I was testing out some equations I found in different places, I got that particular system from here: https://www.youtube.com/watch?v=OUO1P5ZgH2s
Thank you for your input.
RE: Fireworks while trying to solve system of equations - Albert Chan - 07-03-2021 08:25 PM
(07-03-2021 07:20 PM)dah145 Wrote: I was testing out some equations I found in different places, I got that particular system from here: https://www.youtube.com/watch?v=OUO1P5ZgH2s
The video assumed log() is really log10().
log(x) vs ln(x) — The curse of scientific computing
HP Prime home mode, both log and LOG meant log10.
CAS mode have different meanings (log = ln, LOG = log10, same as XCAS)
CAS> fsolve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z]=[1,1,1])
[0.281669416538, 1.23071511956, 0.75280920719]
CAS> fsolve([z^3=y^2*x,sqrt(x)=LOG(3*z^2),5*z*x=y^x],[x,y,z]=[1,1,1])
[0.235667688071, 2.0897828558, 1.00964210847]
RE: Fireworks while trying to solve system of equations - dah145 - 07-04-2021 01:51 AM
(07-03-2021 08:25 PM)Albert Chan Wrote:(07-03-2021 07:20 PM)dah145 Wrote: I was testing out some equations I found in different places, I got that particular system from here: https://www.youtube.com/watch?v=OUO1P5ZgH2s
The video assumed log() is really log10().
log(x) vs ln(x) — The curse of scientific computing
HP Prime home mode, both log and LOG meant log10.
CAS mode have different meanings (log = ln, LOG = log10, same as XCAS)
CAS> fsolve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z]=[1,1,1])
[0.281669416538, 1.23071511956, 0.75280920719]
CAS> fsolve([z^3=y^2*x,sqrt(x)=LOG(3*z^2),5*z*x=y^x],[x,y,z]=[1,1,1])
[0.235667688071, 2.0897828558, 1.00964210847]
Duly noted, thanks.