hello all,

I have a tough past exam question that I can not seem to fully understand. If we use newtons method to approx $\displaystyle \sqrt(a)$ by looking for the 0 of the function $\displaystyle f$ defined by $\displaystyle f(x) = x^2 - a$, the sequence $\displaystyle \{x_n\}$ as $\displaystyle n=1$ to $\displaystyle \infty$ is generated, where $\displaystyle x_1$ = 1 and $\displaystyle x_{n+1}$ = $\displaystyle \frac{1}{2}(x_n+\frac{a}{x_n})$.

The question states that show that if:

$\displaystyle 0<x_m<\sqrt(a)$, then $\displaystyle x_{m+1}>\sqrt(a)$.

- Hint: add $\displaystyle x_{m+1}-\sqrt(a)$, and complete the square.

Not sure how to approach this one, but using the hint would I do something like..

$\displaystyle \frac{1}{2}(x_m+\frac{a}{m_n})-\sqrt(a)$ = $\displaystyle \frac{x_m}{2}+\frac{a}{m_n} - \sqrt(a)$ ..

Thanks..