1.11: Show that where and are integers to be found.

(a) Show that $\displaystyle \sqrt{4-x} = A\left(1 - \frac{x}{B}\right)^2$ where $\displaystyle A$ and $\displaystyle B$ are integers to be found.

(b) Hence expand $\displaystyle \sqrt{4-x}$ in ascending powers of $\displaystyle x$ up to and including the term in $\displaystyle x^3$
Give each coefficient as an exact fraction in its lowest terms.

(c) Use your expansion with a suitable value of $\displaystyle x$ to obtain an estimate of $\displaystyle \frac{\sqrt{305}}{10}$
Give your answer correct to 5 decimal places.