finding implicit function

[PaulKraemer]

Hi,

I am stuck on the following problem:

Find at least one implicit function f determined by the equation

x^2 - 2xy + y^2 = x

I assume that I have to solve the above equation for y, but I can't figure out how to do it.

If anyone could give me a clue, I'd really appreciate it.

Thanks in advance,
Paul

 

[tkhunny]

I might try completing the square or the quadratic formula.

One mustn't forget ones algebra!

 

[JeffM]

Hi,

I am stuck on the following problem:

Find at least one implicit function f determined by the equation

x^2 - 2xy + y^2 = x

I assume that I have to solve the above equation for y, but I can't figure out how to do it.

If anyone could give me a clue, I'd really appreciate it.

Thanks in advance,
Paul

Technically I think x[sup:jjokig71]2[/sup:jjokig71] - x - 2xy + y[sup:jjokig71]2[/sup:jjokig71] = 0 is an implicit function. You cannot tell from that which is the dependent or independent variable.

Probably that answer is not what is desired, however.

If it is understood that x is the independent variable and y the dependent, it is fairly easy to find x = g(y) although g(y) is not unique.

x^2 - 2xy + y^2 = x.

So, (x - y)^2 = x.

So, [(x - y)^2]^(1/2) = x^(1/2).

You take it from there.

 

[PaulKraemer]

Thanks JeffM and tkhunny -

I appreciate your help!

Paul