It doesn't really matter, but by using the simpfuncs option, the square root can be
denested by the solver:
(%i3) (load(to_poly_solver), load(sqdnst))$
(%i4) %solve(sqrt(3-sqrt(x-1))-sqrt(x-sqrt(2)),x, 'simpfuncs = ['sqrtdenest]);
(%o4) %union([x=3])
--Barton
________________________________
From: maxima-bounces at math.utexas.edu [maxima-bounces at math.utexas.edu] on behalf of Stavros Macrakis [macrakis at alum.mit.edu]
Sent: Monday, August 20, 2012 10:22
To: Igor
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Step by step
The solve command doesn't handle cases like this, but %solve does:
load(to_poly_solve)$
eq: sqrt(3-sqrt(x-1))-sqrt(x-sqrt(2))$
sols: %solve(eq,x);
sol: part(sols,1,1,2) <<< extract the one solution from the Union expression
sol =>
-(sqrt(2^(5/2)+9)-2^(3/2)-7)/2
Messy, eh? float(sol) seems to be equal to 3. None of Maxima's standard simplifiers (ratsimp, radcan) can reduce this to 3, but Maxima does have a special simplifier for square root denesting:
load(sqdnst)$
sqrtdenest(sol) => 3
This doesn't give you a 'step-by-step' solution, though.
I wonder, too, if sqrtdenest shouldn't be either part of the general simplifier or of radcan....
-s
On Sun, Aug 19, 2012 at 4:37 PM, Igor <igor at iuav.it<mailto:igor at iuav.it>> wrote:
Dear,
Who can help me?
I need a step by step solution of the following equation: sqrt(3-sqrt(x-1))-sqrt(x-sqrt(2)).
The only result I get is the following: sqrt(x-sqrt(2))=sqrt(3-sqrt(x-1)).
Now, how can i get a right result for x by a step by step solution?
Many many thanks.
Igor
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