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 http://www3.wolframalpha.com/input/?i=0.2%3D(x%2B1)^(1%2F2)-x^(1%2F2)
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 http://www3.wolframalpha.com/input/?i=0.2%3D(x%2B1)^(1%2F2)-x^(1%2F2)
$\displaystyle \sqrt{x+1} - \sqrt{x} = \frac{1}{5}$
square both sides ...
$\displaystyle (x+1) - 2\sqrt{x(x+1)} + x = \frac{1}{25}$
combine like terms ...
$\displaystyle 2x + \frac{24}{25} = 2\sqrt{x(x+1)}$
$\displaystyle x + \frac{12}{25} = \sqrt{x(x+1)}$
square both sides again ...
$\displaystyle x^2 + \frac{24x}{25} + \frac{144}{625} = x(x+1)$
combine like terms ...
$\displaystyle \frac{144}{625} = \frac{x}{25}$
$\displaystyle \frac{144}{25} = x$
btw ... this is not an exponential equation, it's a radical equation.