• May 22nd 2012, 04:43 PM
Hi guys, I was going through my book to refresh my calc 2 material and I saw this, anyone know how they got to the answer x=144/25? Thank you (Hi) http://www3.wolframalpha.com/input/?i=0.2%3D(x%2B1)^(1%2F2)-x^(1%2F2)
• May 22nd 2012, 04:59 PM
skeeter
$\sqrt{x+1} - \sqrt{x} = \frac{1}{5}$

square both sides ...

$(x+1) - 2\sqrt{x(x+1)} + x = \frac{1}{25}$

combine like terms ...

$2x + \frac{24}{25} = 2\sqrt{x(x+1)}$

$x + \frac{12}{25} = \sqrt{x(x+1)}$

square both sides again ...

$x^2 + \frac{24x}{25} + \frac{144}{625} = x(x+1)$

combine like terms ...

$\frac{144}{625} = \frac{x}{25}$

$\frac{144}{25} = x$

btw ... this is not an exponential equation, it's a radical equation.
• May 22nd 2012, 05:04 PM