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May 18th, 2015, 01:14 PM   #1
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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)
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May 18th, 2015, 01:41 PM   #2
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Originally Posted by DreamFall View Post
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, $\displaystyle \frac{x-1}{x} = 0$

$\displaystyle x = 1$
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May 18th, 2015, 02:00 PM   #3
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I didnt understand the steps
could u elebarete? and btw there are 2 solutions.
1 of them is 1.
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May 18th, 2015, 03:37 PM   #4
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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.
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May 18th, 2015, 04:17 PM   #5
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Quote:
Originally Posted by DreamFall View Post
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
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May 18th, 2015, 05:28 PM   #6
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Quote:
Originally Posted by skeeter View Post
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 ...

$\displaystyle \sqrt{x-\frac{1}{x}} - \sqrt{1-\frac{1}{x}}$
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May 19th, 2015, 03:55 AM   #7
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Quote:
Originally Posted by skeeter View Post
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)
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May 19th, 2015, 04:40 AM   #8
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the answers are: 1 and phi=golden ratio
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May 19th, 2015, 04:41 AM   #9
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the answers are: 1 and phi=golden ratio
Could u show the steps? cant figure it out
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