Originally Posted by

**kezman** This problem I think it can be soved with Lagrange multipliers but I tried to solve this with out them.

Find the maximum and minimum values of the variable x on the Equation:

$\displaystyle 4y^{2}-2xy+x^{2}=3 $

I dont know if Im having all the solutions when I solve for y:

$\displaystyle (2y - \frac{1}{2}x)^{2}+\frac{3}{4}x^2=3$

$\displaystyle y = \dfrac{\sqrt{3 - \frac{3}{4}x^{2}} + \frac{1}{2}x}{2} $

For which I ask:

$\displaystyle \sqrt{3 - \frac{3}{4}x^{2}} > 0 $

Solving it I have:

$\displaystyle |x| > 2 $