My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Thanks Tree5Thanks
Reply
 
LinkBack Thread Tools Display Modes
April 24th, 2018, 08:30 AM   #11
Global Moderator
 
Joined: Dec 2006

Posts: 20,617
Thanks: 2072

Partly experience, in that it’s quite handy to have seen such a question before, but inspection would help as well. In your answer to my question, the absolute value isn’t needed. Consider also what you get if my expression has the “+” symbol replaced by a “-“ symbol.
Thanks from bongcloud
skipjack is offline  
 
April 24th, 2018, 10:15 AM   #12
Newbie
 
Joined: Apr 2018
From: Banovo Brdo

Posts: 12
Thanks: 0

Do you mean $1+\sqrt{\frac{x-a}{a}}+\frac{1}{4}\lvert{\frac{x-a}{a}}\rvert$? Yes, I've realized that here:
Quote:
Originally Posted by bongcloud View Post
I see. If we assume solution is $\mathbb{R}$, then $x-a\geq 0 \implies x\geq a$
I don't see how to proceed from there, though. For example, if I get rid of the roots, I'm left with $1+\frac{1}{2}\sqrt{\frac{x-a}{a}}+\lvert 1-\frac{1}{2}\sqrt{\frac{x-a}{a}}\rvert$
While typing this, I've realized I'd been a victim of poor rewriting skills yet again.
However, it seems to me that we need to replace $\left(1-\frac{1}{2}\sqrt{\frac{x-a}{a}}\right)^2$ with $\left(\frac{1}{2}\sqrt{\frac{x-a}{a}}-1\right)^2
$.

Then we have
$
\left\lvert \frac{1}{2}\sqrt{\frac{x-a}{a}}-1\right\rvert=\left\{\begin{aligned}
&\frac{1}{2}\sqrt{\frac{x-a}{a}}-1, &&\frac{1}{2}\sqrt{\frac{x-a}{a}}-1\geq 0\implies x\geq 5a\\
&1-\frac{1}{2}\sqrt{\frac{x-a}{a}}, &&\frac{1}{2}\sqrt{\frac{x-a}{a}}-1<0\implies a\leq x<5a
\end{aligned}
\right.
$

Which produces the same solution set as in #9

$
E=\left\{\begin{aligned}
&2, &&5a\geq x>a\\
&\sqrt{\frac{x-a}{a}}, &&x\geq 5a
\end{aligned}
\right.
$

Am I missing something?
By the way, I appreciate your maieutic approach to teaching.

Last edited by bongcloud; April 24th, 2018 at 10:40 AM.
bongcloud is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
expression, simplify



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
simplify the expression Help123 Calculus 3 January 8th, 2018 03:02 PM
Simplify the expression Chikis Algebra 4 December 18th, 2015 02:18 AM
Simplify the Expression jaredbeach Algebra 2 September 2nd, 2011 09:00 AM
Simplify this expression football Algebra 4 March 14th, 2011 08:48 AM
Simplify the Expression jaredbeach Calculus 1 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.