## How to extract square roots

Q: Extract the square roots of (i) $\frac{a^2}{x^2} -ax + \frac{6a}{x}+11+ \frac{x^2}{a^2}+ \frac{6x}{a}$ (ii) $\frac{c^{4}}{4} +cx + \frac{x^{2}}{c^{2}} +\frac{1}{4x^{2}} + \frac{c^{2}}{2x} + \frac{1}{c}$

oi decided to follow skeeter's advice How to extract square root of three or more terms?

(i) $\frac{a^2}{x^2} -ax + \frac{6a}{x}+11+ \frac{x^2}{a^2}+ \frac{6x}{a}$
if t is reducible the quadratic will have a root therefore
$\frac{a^2}{x^2} -ax + \frac{6a}{x}+11+ \frac{x^2}{a^2}+ \frac{6x}{a} = (g\frac{a}{x} + b\frac{x}{a})^2$

where b, g are constant

$\frac{a^2}{x^2} -ax + \frac{6a}{x}+11+ \frac{x^2}{a^2}+ \frac{6x}{a} = (g^2\frac{a^2}{x^2} + 2gb + b^2\frac{x^2}{a^2})$
i get stuck because i cannot find the square of 11 or the right identity to use to extract the square root

(ii) i cannot find the right identity to use to extract the square root