### Equation!

Posted:

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

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Posted: **Tue Jun 05, 2012 10:53 am**

Find all real solution of \[\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\].

Posted: **Wed Jun 06, 2012 11:48 am**

$The$ $only$ $solution$ $is$ $x=5$ .

Posted: **Wed Jun 06, 2012 2:34 pm**

Ooops...there are more solutions.

Posted: **Wed Jun 06, 2012 2:50 pm**

Actually,$5\leq x\leq 10$

Posted: **Fri Jun 08, 2012 12:41 am**

Yes. Your answer is correct. But please post the solution(either fully or in brief)

Posted: **Mon Sep 09, 2013 12:36 pm**

The equation is equivalent to $|\sqrt{x-1}-2|+|\sqrt{x-1}-3|=1$.SANZEED wrote:Find all real solution of \[\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\].

From here we use the inequality $|a|+|b| \ge |a+b|$.