ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 06 Nov 2013 20:58:07 +0100equation sqrthttps://ask.sagemath.org/question/10710/equation-sqrt/I tried to solve with sage $$4=x+\sqrt{(x+1)(x+2)}+\sqrt{(x+2)(x+3)}+\sqrt{(x+3)(x+1)}$$
but it does work.
Could you help me what shoud I enter in sage to get exact solution ?
thank youWed, 06 Nov 2013 18:31:54 +0100https://ask.sagemath.org/question/10710/equation-sqrt/Answer by Shashank for <p>I tried to solve with sage $$4=x+\sqrt{(x+1)(x+2)}+\sqrt{(x+2)(x+3)}+\sqrt{(x+3)(x+1)}$$
but it does work.
Could you help me what shoud I enter in sage to get exact solution ?
thank you</p>
https://ask.sagemath.org/question/10710/equation-sqrt/?answer=15673#post-id-15673I don't think this equation can be solved analytically, but I may be wrong. Here is how I found the solution.
I used the following command to plot the function
plot(x+sqrt((x+1)*(x+2))+sqrt((x+2)*(x+3)+sqrt((x+3)*(x+1)))-4,x,-10,10)
I see that this is zero at two points near -7 and 0. So I typed the following commands to find the root in that region
find_root(x+sqrt((x+1)*(x+2))+sqrt((x+2)*(x+3)+sqrt((x+3)*(x+1)))-4,-1,5)
find_root(x+sqrt((x+1)*(x+2))+sqrt((x+2)*(x+3)+sqrt((x+3)*(x+1)))-4,-10,05)
This gave me -0.06139800265618307 and -7.529020910031573.Wed, 06 Nov 2013 20:58:07 +0100https://ask.sagemath.org/question/10710/equation-sqrt/?answer=15673#post-id-15673