2 Algebraic Equations

**Nash55** · December 3rd 2007, 11:56 AM

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

**Nash55** · December 3rd 2007, 12:59 PM

If someone could help I'd be very grateful. Thanks.

**Jhevon** · December 3rd 2007, 01:58 PM

Originally Posted by Nash55

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

8-sqrt(y-1)=6

$8 - \sqrt{y - 1} = 6$

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

now, square both sides and continue

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

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

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

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

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

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