I've been stuck on these two. If you could help me and show the work. Thanks.

8-sqrt(y-1)=6

x^2/3-10x^1/3+9=0

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- Dec 3rd 2007, 11:56 AMNash552 Algebraic Equations
I've been stuck on these two. If you could help me and show the work. Thanks.

8-sqrt(y-1)=6

x^2/3-10x^1/3+9=0 - Dec 3rd 2007, 12:59 PMNash55
If someone could help I'd be very grateful. Thanks.

- Dec 3rd 2007, 01:58 PMJhevon
$\displaystyle 8 - \sqrt{y - 1} = 6$

$\displaystyle \Rightarrow - \sqrt {y - 1} = -2$

now, square both sides and continue

Quote:

x^2/3-10x^1/3+9=0

$\displaystyle \left( x^{1/3} \right)^2 - 10 \left( x^{1/3} \right) + 9 = 0$

this is quadratic in $\displaystyle x^{1/3}$. this becomes as clear as day if we say let $\displaystyle x^{1/3} = y$, then we get

$\displaystyle y^2 - 10y + 9 = 0$

now solve for y. when done, replace y with $\displaystyle x^{1/3}$ and then solve for x