David Billinghurst wrote:
> Russell Shaw wrote:
>> Hi,
>> Starting with:
>>
>> x = sqrt(x^2 + 1) - a
>>
>> How do i get it into the form:
>>
>> x^2(b^2 - 1) + 2*a*b*x + a^2 - 1 = 0
>>
>>
>> Also, i tried to solve for x:
>>
>> 2
>> (%o1) x = sqrt(x + 1) + a
>>
>> (%i2) solve(%, x);
>>
>>
>> It just gives:
>> 2
>> (%o2) [x = sqrt(x + 1) + a]
>>
>> I've read all the manuals.
>>
> You can solve it "by hand" using maxima. Where does where b come into it?
Hi David.B,
It should have been: x = (sqrt(x^2 + 1) - a)/b
Too many hours staring at manuals and stuff.
> (%i1) x=sqrt(x^2+1)-a;
> 2
> (%o1) x = sqrt(x + 1) - a
> (%i2) %+a;
> 2
> (%o2) x + a = sqrt(x + 1)
> (%i3) lhs(%)^2=rhs(%)^2;
> 2 2
> (%o3) (x + a) = x + 1
> (%i4) expand(%);
> 2 2 2
> (%o4) x + 2 a x + a = x + 1
> (%i5) lhs(%)-rhs(%)=0;
> 2
> (%o5) 2 a x + a - 1 = 0
> (%i6) solve(%,x);
> 2
> a - 1
> (%o6) [x = - ------]
> 2 a
I had thought of manually solving it like this, but was wondering if
there was a more automated way of solving for x, because the example
is a simpler form of a larger messier equation i was working on.
I was also unsure how to manipulate equations manually in maxima
that well having found Maxima a few days ago, but your example
makes it clear.