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
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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.
Hello, sscgeek!
$\displaystyle \text{Solve: }\: \frac{x + \sqrt{x^2-1}}{x - \sqrt{x^2-1}} + \frac{x - \sqrt{x^2-1}}{x + \sqrt{x^2-1}}\;=\;14$
. . $\displaystyle (a)\;+8 \qquad (b)\;-6 \qquad (c)\;\pm 2 \qquad (d)\; \pm4$
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)