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# equation sqrt

Anonymous

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

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I 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.

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Asked: 2013-11-06 18:31:54 +0200

Seen: 490 times

Last updated: Nov 06 '13