Skip to main content
R
rkok1-Visitor
1-Visitor
May 14, 2016
Question

Can mathcad solf this

  • May 14, 2016
  • 6 replies
  • 3154 views

‌i am new to mathcad and want to know if mathcad can solf a quadratic system like this And know how many answers it gives.

2x1^2-x1+x2^2-3x2+4x3^2+5x3=53

x1^2+3x1-2x2^2+x2-2x3^2+x3=-17

-x1^2-3x1+2x2^2-4x2+x3^2-x3=2

THanks

6 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
May 16, 2016

Try this but I think you must use a numerical not symbolic solution use (Find function)

A
AlanStevens19-Tanzanite
19-Tanzanite
May 16, 2016

You can get two sets of real number solutions as follows (I've used M15):

threequads1.PNG

threequads2.PNG

threequads3.PNG

Alan

W
Werner_E25-Diamond I
25-Diamond I
May 16, 2016

On contrary to the example Valery posted in your system you have summands linear in x1, x2, x3, too.

This would mean that Mathcad has to solve a generic equation of eight order for which no general solution exists.

Therefore I guess the symbolic solver will fail and you have to resort to a numeric solve block which gives you just one solution triple depending on the guess values you have to provide. Different guesses may give you different solutions.

WE

EDIT: Looks like I was a bit late as Alan already solved the problem in an elegant way.

For completeness sake here are all eight solutions (just found by trying different guesses 😉

-
-MFra-21-Topaz II
21-Topaz II
May 16, 2016

Hi Rob. If you like programming, you can solve your system in this way:

Newton in several variables.jpg

Newton in several variables Prime 3.1.jpg

W
Werner_E25-Diamond I
25-Diamond I
May 16, 2016

The system has eight solutions (see above) not four.

Given that all coefficients are real, with any complex solution the conjugate is solution, too.

So you just missed the first set of complex solutions given in my answer above.

But probably Rob is interested in the two real solutions only anyway.

WE

A
AlanStevens19-Tanzanite
19-Tanzanite
May 16, 2016

‌The method I adopted can be extended to find all 8 roots by making use of the function polyroots to find the roots of f(_z1).

ALan

-
-MFra-21-Topaz II
21-Topaz II
May 17, 2016

I would be pleased if you were also interested in another similar example in which the search of the roots is more difficult:

Newton in several variables Prime 3.1 example2.jpg

R
rkok1-VisitorAuthor
1-Visitor
May 20, 2016

‌thank you

Terms & ConditionsAccessibility statement