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lvl10720-Turquoise
20-Turquoise
May 1, 2025
Solved

x + x*(2*x - x^2)^(1/2) + (2*x - x^2)^(1/2) - 1 solve , x ----> ? (Symbolic Evaluate)

Hello Everyone.
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Symbolic Evaluate.PNG


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       Symbolic Evaluate ? ( MC 15 )
Thanks in advance.
Regards.

Werner_E
Werner_EAnswer
25-Diamond I
May 1, 2025

This happens (more often) in MC15 as well that f(x) can't be simplified to 0 or a certain value c we know the expression should simplify to.

Also f(x)-c usually won't simplify to zero but most of the time the symbolics is able to simplify the Boolean expression f(x)=c to 1. Not sure why.

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14 replies

Werner_E
Werner_E25-Diamond I
25-Diamond I
May 1, 2025

Here you are, sure very informative and useful 🙂

Werner_E_1-1746119745429.png

 

BTW, the symbolics in Prime 10 doesn't even try to get an exact symbolic solution

Werner_E_2-1746119878641.png

 

 

 

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lvl10720-TurquoiseAuthor
20-Turquoise
May 1, 2025

***.xmcd file, please.

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Werner_E
Werner_E25-Diamond I
25-Diamond I
May 1, 2025

Here you are

 

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LucMeekes23-Emerald IV
23-Emerald IV
May 1, 2025

Ah, no problem in Mathcad 11 (NOT Prime 11). Here are the four solutions:

LucMeekes_0-1746120511308.png

Their numerical values are:

LucMeekes_1-1746120555520.png

Success!
Luc

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lvl10720-TurquoiseAuthor
20-Turquoise
May 1, 2025

My MC15 say :

Symbolic Evaluate 2.PNG

 3.PNG

and I don't understand the solution of 1.947 ( see my graph below )

4.PNG

 

Thanks any way, Luc.😊

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Werner_E
Werner_E25-Diamond I
25-Diamond I
May 1, 2025

and I don't understand the solution of 1.947 ( see my graph below )

😊

Maple in MC11 seems to be internally squaring the equation and so comes up with four solutions - similar to my modified appraoch here:

Re: x + x*(2*x - x^2)^(1/2) + (2*x - x^2)^... - PTC Community

Unfortunately, MC11 does not remove the invalid dummy solutions. See my reply to Luc below which shows where the 1.947 stems from.

 

By the way, Uncle Wolfram is also content with a numerical approximation only ...

Werner_E_0-1746129647133.png

 

.

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