Vector parameterization of intersection of 2 surfaces

[musicmar]

Homework Statement

Find a vector parameterization of the intersection of the surfaces x²+y⁴+2z³=6 and x=y² in R³.

The Attempt at a Solution

I let x=t.
Then y³=t

I solved the first equation for z in terms of x
z = cube root ((t²+(t(cube rt(t)) - 6)/-2)

I know this is wrong because I checked the back of the book, but I'm not sure how to do it correctly.
Thank you!

 

[gabbagabbahey]

I let x=t.
Then y³=t

Is your 2nd surface x=y^2 or x=y^3?

In either case, to avoid taking sqare roots and cube roots of stuff, try letting y=t instead and solving for x.

 

[musicmar]

x=y³, sorry.

So, when y=t, x=t³
and z= cube rt ((-1/2)(t⁶+t⁴-6))

This is still wrong. The answer is <t²,t,cube rt(3-t⁴)>
It doesn't help that I know the answer unless I know how to do it, though.

 

[gabbagabbahey]

x=y³, sorry.

So, when y=t, x=t³
and z= cube rt ((-1/2)(t⁶+t⁴-6))

This is still wrong. The answer is <t²,t,cube rt(3-t⁴)>
It doesn't help that I know the answer unless I know how to do it, though.

Judging from the answer, it looks as though the 2nd surface is supposed to be x=y^2, so I'd double check the question if I were you.

 

[musicmar]

thank you. you were right, it was x=y^2.