Solving equations in a given range
03-23-2020, 05:14 PM
Post: #1
 Jan 11 Junior Member Posts: 25 Joined: Mar 2020
Solving equations in a given range
I solve the equation TAN (3x) = - x ^ 2 + 3.
The calculator gives six solutions in the range {-3,633 to 2,695}. OKAY. When we set the range of solutions in the range x = 0 to 10, he will give all the solutions correctly. OKAY. Next, when we set x = 10 to 15, it will give only two solutions. However, there are 4 solutions. Now I set the range x = 25 to 30. HP Prime finds no solution. There are as many as 5 solutions in this range.
I checked how the TI-Nspire CX II-T calculator does it. I do all the examples great, perfectly. See this in the attached screenshots of both calculators.

03-24-2020, 07:00 PM
Post: #2
 parisse Senior Member Posts: 1,186 Joined: Dec 2013
RE: Solving equations in a given range
That's because the default step for the bisection solver is too large to detect the roots. You can obtain more solutions by adding an optional argument, like this
solve(tan(3x)=-x^2+3,x=10..15,xstep=0.001)
or
solve(tan(3x)=-x^2+3,x=25..30,10000)
03-24-2020, 07:25 PM
Post: #3
 Jan 11 Junior Member Posts: 25 Joined: Mar 2020
RE: Solving equations in a given range
Dear Parisse. Thank you very much for very valuable advice. I've never heard of it. Great, all equations have been solved. Thank you again.
03-24-2020, 08:13 PM
Post: #4
 parisse Senior Member Posts: 1,186 Joined: Dec 2013
RE: Solving equations in a given range
I have just increased the default number of steps, this will detect more solutions if the optional argument is not given.
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