can anyone help me:
Convert the polar equation r^2=3 cos(2x)
I assume that you mean convert to cartesians.
Remember that $\displaystyle x = r\cos{\theta}$, $\displaystyle y = r\sin{\theta}$ and $\displaystyle x^2 + y^2 = r^2$.
So $\displaystyle r^2 = 3\cos{2\theta}$
$\displaystyle r^2 = 3(\cos^2{\theta} - \sin^2{\theta})$
$\displaystyle r^2 = 3\left[\left(\frac{x}{r}\right)^2 - \left(\frac{y}{r}\right)^2\right]$
$\displaystyle r^2 = 3\left[\frac{x^2}{r^2} - \frac{y^2}{r^2}\right]$
$\displaystyle r^2 = \frac{3x^2 - 3y^2}{r^2}$
$\displaystyle r^4 = 3x^2 - 3y^2$
$\displaystyle (x^2 + y^2)^2 = 3x^2 - 3y^2$
$\displaystyle x^4 + 2x^2y^2 + y^4 = 3x^2 - 3y^2$