Equation!

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SANZEED
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Equation!

Unread post by SANZEED » 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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sakibtanvir
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Re: Equation!

Unread post by sakibtanvir » Wed Jun 06, 2012 11:48 am

$The$ $only$ $solution$ $is$ $x=5$ .
Last edited by sakibtanvir on Wed Jun 06, 2012 2:49 pm, edited 1 time in total.
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sakibtanvir
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Re: Equation!

Unread post by sakibtanvir » Wed Jun 06, 2012 2:34 pm

Ooops...there are more solutions.
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sakibtanvir
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Re: Equation!

Unread post by sakibtanvir » Wed Jun 06, 2012 2:50 pm

Actually,$5\leq x\leq 10$
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SANZEED
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Re: Equation!

Unread post by SANZEED » Fri Jun 08, 2012 12:41 am

Yes. Your answer is correct. But please post the solution(either fully or in brief)
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harrypham
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Re: Equation!

Unread post by harrypham » 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 $|a|+|b| \ge |a+b|$.

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