SOLUTION: I need help solving the following for y in terms of x: x = y^4 + y^2 + 1 I can't think of much that I can do to it that is useful. What I have considered is that: x

Question 143815: I need help solving the following for y in terms of x:

x = y^4 + y^2 + 1

I can't think of much that I can do to it that is useful. What I have considered is that:

x-1 = y^4 + y^2 = y^2(y^2 + 1)

and I could make a substitution u=y^2 so:

x-1 = u(u+1)

but again, I don't see the value in it if there is any. Perhaps it would help if I put this in context. This is from a calculus problem where I am to find dy/dx in terms of x. The idea is to find:

dx/dy = 1/[4y^3 + 2y] or [4y^3 + 2y]^(-1) and subsitute the y in terms of x which we solved above. As you can see, the difficult part is the algebra solving for y in terms of x. Any help would be much appreciated.

Greg
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Let . So

Plug in and

Complete the square to convert into (if you need help completing the square, check out this solver)

Subtract from both sides

Take the square root of both sides

Subtract from both sides

Rearrange the terms

Replace "u" with

Take the square root of both sides

So transforms into
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