# Math Help - Indicies and Substitution

1. ## Indicies and Substitution

if you take y=x^1/3, find the values of x, if x^1/3 - 2x^-1/3= 1

2. $x^{1/3} - 2x^{-1/3}= 1$
$x^{1/3} - \frac{2}{x^{1/3}}= 1$
$x^{2/3} - x^{1/3} - 2= 0$
$x^{1/3} = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot -2}}{2 \cdot 1}$
$x^{1/3} = \frac{1 \pm 3}{2}$
$x = (\frac{1 \pm 3}{2})^3$

3. Originally Posted by will_akrigg

if you take y=x^1/3, find the values of x, if x^1/3 - 2x^-1/3= 1
$y=x^{\frac{1}{3}}$

$x^{\frac{1}{3}}-2x^{-\frac{1}{3}}=1$

Substituting,

$y-\frac{2}{y}=1$

$y^2-2=y$

$y^2-y-2=0$

$(y-2)(y+1)$

$y=2 \ \ or \ \ y=-1$

Substituting back into $y=x^{\frac{1}{3}}$, we get

$x^{\frac{1}{3}}=2$

$\boxed{x=8}$

$x^{\frac{1}{3}}=-1$

$\boxed{x=-1}$