On Sun, 19 Aug 2012, Igor 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
(%i1) eq:sqrt(3-sqrt(x-1))-sqrt(x-sqrt(2))=0$
(%i2) solve(eq, [x])[1];
(%o2) sqrt(x-sqrt(2))=sqrt(3-sqrt(x-1))
(%i3) %^2;
(%o3) x-sqrt(2)=3-sqrt(x-1)
(%i4) solve(%,sqrt(x-1))[1];
(%o4) sqrt(x-1)=-x+sqrt(2)+3
(%i5) %^2,expand;
(%o5) x-1=x^2-2^(3/2)*x-6*x+3*2^(3/2)+11
(%i6) sols:solve(%,x);
(%o6) [x=3,x=2^(3/2)+4]
(%i7) solution:sublist(sols,lambda([e],is(ev(eq,e))));
(%o7) [x=3]
Aleksas D
*