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### Equation!

Posted: Tue Jun 05, 2012 10:53 am
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
$The$ $only$ $solution$ $is$ $x=5$ .

### Re: Equation!

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

### Re: Equation!

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

### Re: Equation!

Posted: Fri Jun 08, 2012 12:41 am
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
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 $|a|+|b| \ge |a+b|$.