Equation!
Find all real solution of \[\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\].
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$
-
- Posts:188
- Joined:Mon Jan 09, 2012 6:52 pm
- Location:24.4333°N 90.7833°E
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.
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.
-
- Posts:188
- Joined:Mon Jan 09, 2012 6:52 pm
- Location:24.4333°N 90.7833°E
Re: Equation!
Ooops...there are more solutions.
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.
-
- Posts:188
- Joined:Mon Jan 09, 2012 6:52 pm
- Location:24.4333°N 90.7833°E
Re: Equation!
Actually,$5\leq x\leq 10$
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.
Re: Equation!
Yes. Your answer is correct. But please post the solution(either fully or in brief)
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$
Re: Equation!
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 $|a|+|b| \ge |a+b|$.