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Equation!

Posted: Tue Jun 05, 2012 10:53 am
by SANZEED
Find all real solution of \[\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\].

Re: Equation!

Posted: Wed Jun 06, 2012 11:48 am
by sakibtanvir
$The$ $only$ $solution$ $is$ $x=5$ .

Re: Equation!

Posted: Wed Jun 06, 2012 2:34 pm
by sakibtanvir
Ooops...there are more solutions.

Re: Equation!

Posted: Wed Jun 06, 2012 2:50 pm
by sakibtanvir
Actually,$5\leq x\leq 10$

Re: Equation!

Posted: Fri Jun 08, 2012 12:41 am
by SANZEED
Yes. Your answer is correct. But please post the solution(either fully or in brief)

Re: Equation!

Posted: Mon Sep 09, 2013 12:36 pm
by harrypham
SANZEED wrote:Find all real solution of \[\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\].
The equation is equivalent to $|\sqrt{x-1}-2|+|\sqrt{x-1}-3|=1$.
From here we use the inequality $|a|+|b| \ge |a+b|$.