Cartesian equation for x=t^2+1 y=t^3+t?

Question

Could anyone help me transform these parametric equations into Cartesian ones? I cant seem to get the right answer as the book 

Answer 1

x = t²+1 y = t³+t

 

Since x = t²+1, t² = x-1.  t = ±√(x-1)  

 

y = t³+t = t(t²+1) = ±x√(x-1)

 

Therefore, y = ±x√(x-1)

 

If we square both sides, we have y² = x²(x-1)

 

                                              y² = x³ - x²

 

Answer 2

 

x = t²+ 1

x - 1 = t²

Sqrt(x - 1) = t

Where x ≥ 1

 

plug it into the other equation for t

y = t³+ t

y = t(t² - 1)

y = Sqrt(x - 1)*(t² - 1)

 

y = Sqrt(x - 1)* (t² - 1)

y = Sqrt(x - 1)*(x - 1 - 1)

 

y = Sqrt(x - 1)*(x - 2)

x ≥ 1