## Need help with this exponential equation.

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
rogermiranda
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Joined: Fri Apr 30, 2010 6:01 pm
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### Need help with this exponential equation.

The equation is x(raised to the one-half) - 6x(raised to the negative one-half) - 5 = 0
x^(1/2) - 6x^(-1/2) - 5 = 0
At this point what I tried to do was change it to a square root. So I get this
sqr of x + sqr of 6x - 5 = 0 At this point I am confused and stuck. Please help. By the way the answer is x = 36

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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### Re: Need help with this exponential equation.

rogermiranda wrote:The equation is x(raised to the one-half) - 6x(raised to the negative one-half) - 5 = 0
x^(1/2) - 6x^(-1/2) - 5 = 0
At this point what I tried to do was change it to a square root. So I get this
sqr of x + sqr of 6x - 5 = 0 At this point I am confused and stuck. Please help. By the way the answer is x = 36

$x^{1/2}-6x^{-1/2}-5=0$

multiply by $\sqrt{x}$

get

$x-6-5\sqrt{x}=0\Leftrightarrow x-5\sqrt{x}-6=0$

let $y^2=x$

then you get

$y^2-5y-6=0$

now solve for $y$ and then determine $x$