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ppal_25568718-Opal
18-Opal
August 1, 2022
Solved

What built in Functionality is Best to Solve this.

Given 

ppal_0-1659316191690.png

Soln x=1 and x=-1

I have tried the solve box - the answer depends on the seed value.

ppal_1-1659316356502.png

 

ppal_2-1659316378789.png

 

 Best approach to solve in Mathcad?  Thanks.

Werner_E
Werner_EAnswer
25-Diamond I
August 1, 2022

A solve block in Prime only uses numerical approximation algorithms and will always give you just one solution which depends on the guess value, as you found out yourself.

The symbolic "solve" should give you all solutions, especially when you combine it with "fully". But the symbolic engine in Prime/Mathcad is to weak and not capable to do so - it yields just one of the two solutions:

Werner_E_0-1659317461826.png

You can plot the LHS and RHS of the equation to see that there are two solutions

Werner_E_1-1659317562809.png

You can also combine different guess values in a vector and so get both solutions in one go

Werner_E_2-1659317622606.png

Its no surprise that Wolfram Alpha does a much better job with this:

Werner_E_3-1659317925019.png

 

I guess that Mathcad 11 (with Maple under the hood) will do a better job, too.

 

 

 

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5 replies

Werner_E
Werner_E25-Diamond IAnswer
25-Diamond I
August 1, 2022

A solve block in Prime only uses numerical approximation algorithms and will always give you just one solution which depends on the guess value, as you found out yourself.

The symbolic "solve" should give you all solutions, especially when you combine it with "fully". But the symbolic engine in Prime/Mathcad is to weak and not capable to do so - it yields just one of the two solutions:

Werner_E_0-1659317461826.png

You can plot the LHS and RHS of the equation to see that there are two solutions

Werner_E_1-1659317562809.png

You can also combine different guess values in a vector and so get both solutions in one go

Werner_E_2-1659317622606.png

Its no surprise that Wolfram Alpha does a much better job with this:

Werner_E_3-1659317925019.png

 

I guess that Mathcad 11 (with Maple under the hood) will do a better job, too.

 

 

 

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    LucMeekes23-Emerald IV
    23-Emerald IV
    August 1, 2022

    "I guess that Mathcad 11 (with Maple under the hood) will do a better job, too."

    Don't set the expectation for that old version of Maple too high:

    LucMeekes_1-1659357919821.png

    Why is the first answer not (just) 1 instead of 1.0000000?

    There's no way to get a negative or complex result from the symbolic solver.

     

    Luc

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    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    August 1, 2022
    @LucMeekes wrote:

    "I guess that Mathcad 11 (with Maple under the hood) will do a better job, too."

    Don't set the expectation for that old version of Maple too high:

     

    Well, it seems that sometimes we glorify the good old things a bit too much. 🤔

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    ValeryOchkov24-Ruby IV
    24-Ruby IV
    August 1, 2022

    1i.png

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    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    August 1, 2022

    Yes, the "root" function can be used, too. And you also can use multiple guesses in one go if you vectorize:

    Werner_E_0-1659345982526.png

    The root function in its variant with four arguments can also be evaluated symbolically, but like the symbolic "solve" it would yield just one of the many solutions and the range for x provided has no effect at all:

    Werner_E_4-1659346507611.png

     

    I found no way to talk Mathcad or Prime into giving a complete closed solution like

    Werner_E_2-1659346282944.png

     

     

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