Equation!

Discussion on Bangladesh National Math Camp
SANZEED
Posts: 550
Joined: Wed Dec 28, 2011 6:45 pm

Equation!

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!

$The$ $only$ $solution$ $is$ $x=5$ .
Last edited by sakibtanvir on Wed Jun 06, 2012 2:49 pm, edited 1 time in total.
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sakibtanvir
Posts: 188
Joined: Mon Jan 09, 2012 6:52 pm
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Re: Equation!

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

Actually,$5\leq x\leq 10$
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SANZEED
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Joined: Wed Dec 28, 2011 6:45 pm

Re: Equation!

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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 $|a|+|b| \ge |a+b|$.