(a) If $n$ is even, the greatest coefficient is $^n{C_{n/2}}$

Therefore the greatest term $ = {\,^n}{C_{n/2}}{x^{n/2}}$

$\therefore \,{\,^n}{C_{n/2}}{x^{n/2}} > {\,^n}{C_{(n/2) – 1}}{x^{(n – 2)/2}}$ and

$^n{C_{n/2}}{x^{n/2}} > {\,^n}{C_{(n/2) + 1}}{x^{(n/2) + 1}}$

==> $\frac{{n – \frac{n}{2} + 1}}{{\frac{n}{2}}}x > 1$and $\frac{{\frac{n}{2}}}{{\frac{n}{2} + 1}}x < 1$

==> $x > \frac{{\frac{n}{2}}}{{\frac{n}{2} + 1}}$ and $x < \frac{{\frac{n}{2} + 1}}{{\frac{n}{2}}}$

==> $x > \frac{n}{{n + 2}}$and $x < \frac{{n + 2}}{n}$