# Important question plzzzzzzz help

• Jun 13th 2013, 12:11 PM
sscgeek
Important question plzzzzzzz help
THE SOLUTION OF

[X + (X^2-1)^1/2 / X - (X^2-1)^1/2] + [ X - (X^2-1)^1/2 / X + (X^2-1)^1/2 ] = 14

a) +8

b) -6

c) + or- 2

d) + or - 4
• Jun 13th 2013, 12:16 PM
MarkFL
Re: Important question plzzzzzzz help
I have a few suggestions for you to get prompt help here:

• Use unique and descriptive topic titles.
• Use proper bracketing symbols or better yet use $\displaystyle \LaTeX$ to make your questions unambiguous.
• Show you work so the helpers here know exactly where you are stuck.
• Jun 13th 2013, 12:41 PM
ebaines
Re: Important question plzzzzzzz help
Quote:

Originally Posted by sscgeek
THE SOLUTION OF

[X + (X^2-1)^1/2 / X - (X^2-1)^1/2] + [ X - (X^2-1)^1/2 / X + (X^2-1)^1/2 ] = 14

What you wrote is this:

$\displaystyle \left [ x+ \frac {\sqrt{x^2-1}} x - \sqrt {x^2-1} \right ] + \left [ x - \frac {\sqrt{x^2-1}} x + \sqrt {x^2-1} \right ] = 14$

Note that many of the terms cancel out, leaving just 2x = 14. So it seems that for the equation you wrote none of the answers are correct.
• Jun 13th 2013, 03:13 PM
Soroban
Re: Important question plzzzzzzz help
Hello, sscgeek!

Quote:

$\displaystyle \text{Solve: }\: \frac{x + \sqrt{x^2-1}}{x - \sqrt{x^2-1}} + \frac{x - \sqrt{x^2-1}}{x + \sqrt{x^2-1}}\;=\;14$

. . $\displaystyle (a)\;+8 \qquad (b)\;-6 \qquad (c)\;\pm 2 \qquad (d)\; \pm4$

We have: .$\displaystyle \frac{(x+\sqrt{x^2-1})^2 + (x-\sqrt{x^2-1})^2} {(x-\sqrt{x^2-1})(x+\sqrt{x^2-1})} \;=\; 14$

. . $\displaystyle \frac{(x^2 + 2x\sqrt{x^2-1} + x^2-1) + (x^2 - 2x\sqrt{x^2-1} + x^2-1)}{x^2 - (x^2-1)} \;=\;14$

. . $\displaystyle \frac{4x^2 - 2}{1} \:=\:14 \quad\Rightarrow\quad 4x^2 \:=\:16 \quad\Rightarrow\quad x^2 \:=\:16$

. . $\displaystyle x \:=\:\pm4$ .Answer (d)
• Jun 13th 2013, 03:54 PM
HallsofIvy
Re: Important question plzzzzzzz help
Interesting. Soroban's interpretation of what sscgeek wrote is quite different from ebaines' interpretation.
• Jun 14th 2013, 07:20 AM
jpritch422
Re: Important question plzzzzzzz help
I would say that Soroban's interpretation is correct (paretheses needed in the equation), though I can see how ebaines could interpret the equation the way he did without the parentheses.
• Jun 14th 2013, 09:11 AM
topsquark
Re: Important question plzzzzzzz help
Quote:

Originally Posted by jpritch422
I would say that Soroban's interpretation is correct (paretheses needed in the equation), though I can see how ebaines could interpret the equation the way he did without the parentheses.

I believe Soroban is right also. Now all we need is the OP's comment about it...

-Dan