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 May 18th, 2015, 01:14 PM #1 Newbie   Joined: May 2015 From: Israel Posts: 4 Thanks: 0 help needed. Hi all new around here. could u please help me solve the next eq. sqrt(x-(1)/(x)) - sqrt(1-(1)/(x)) = (x-1)/(x) May 18th, 2015, 01:41 PM   #2
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 Originally Posted by DreamFall Hi all new around here. could u please help me solve the next eq. sqrt(x-(1)/(x)) - sqrt(1-(1)/(x)) = (x-1)/(x)
You sure the left side of the equation is correct? If so ...

$\displaystyle \sqrt{x-\frac{1}{x}} - \sqrt{1-\frac{1}{x}} = 0$

so, $\displaystyle \frac{x-1}{x} = 0$

$\displaystyle x = 1$ May 18th, 2015, 02:00 PM #3 Newbie   Joined: May 2015 From: Israel Posts: 4 Thanks: 0 I didnt understand the steps could u elebarete? and btw there are 2 solutions. 1 of them is 1. May 18th, 2015, 03:37 PM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Your equation is $\displaystyle \sqrt{x- \frac{1}{x}}- \sqrt{1- \frac{1}{x}}= 0$. Adding $\displaystyle \sqrt{1- \frac{1}{x}}$ to both sides: $\displaystyle \sqrt{x- \frac{1}{x}}= \sqrt{1- \frac{1}{x}}$ Squaring both sides, $\displaystyle x- \frac{1}{x}= 1- \frac{1}{x}$. Add $\displaystyle \frac{1}{x}$ to both sides: $\displaystyle x= 1$. I do NOT see a second solution. What reason do you have to say there are two solutions? Last edited by Country Boy; May 18th, 2015 at 03:40 PM. May 18th, 2015, 04:17 PM   #5
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 Originally Posted by DreamFall I didnt understand the steps could u elebarete? and btw there are 2 solutions. 1 of them is 1.
Are you perhaps looking at the graph? (See below.) It appears there is a solution at x = 0 as well as at x = 1, but we have the exclude the x = 0 because 1/x --> 1/0 in the equation doesn't exist.

-Dan
Attached Images Sqrt.jpg (24.9 KB, 2 views) May 18th, 2015, 05:28 PM   #6
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 Originally Posted by skeeter You sure the left side of the equation is correct? If so ... $\displaystyle \sqrt{x-\frac{1}{x}} - \sqrt{1-\frac{1}{x}} = 0$ so, $\displaystyle \frac{x-1}{x} = 0$ $\displaystyle x = 1$
my error ... I read

$\displaystyle \sqrt{x-\frac{1}{x}} - \sqrt{x-\frac{1}{x}}$

instead of what you (and I) typed ...

$\displaystyle \sqrt{x-\frac{1}{x}} - \sqrt{1-\frac{1}{x}}$ May 19th, 2015, 03:55 AM   #7
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 Originally Posted by skeeter my error ... I read $\displaystyle \sqrt{x-\frac{1}{x}} - \sqrt{x-\frac{1}{x}}$ instead of what you (and I) typed ... $\displaystyle \sqrt{x-\frac{1}{x}} - \sqrt{1-\frac{1}{x}}$
and it isnt = 0 as well. it = 1+x/x

sqrt(x-(1)/(x)) - sqrt(1-(1)/(x)) = (x-1)/(x) May 19th, 2015, 04:40 AM #8 Senior Member   Joined: Nov 2010 Posts: 288 Thanks: 1 the answers are: 1 and phi=golden ratio May 19th, 2015, 04:41 AM   #9
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 Originally Posted by islam the answers are: 1 and phi=golden ratio
Could u show the steps? cant figure it out Tags needed Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post cfg Algebra 8 August 21st, 2013 12:47 AM mathnoob99 Calculus 1 July 1st, 2010 10:27 AM nicky Algebra 7 June 20th, 2010 06:40 PM mathnoob99 Calculus 4 June 10th, 2010 06:40 PM mohit.choudhary Advanced Statistics 3 June 11th, 2009 01:52 PM

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