Use the binomial expansion, in ascending powers of \(x\), to show that
$$\sqrt { ( 4 - x ) } = 2 - \frac { 1 } { 4 } x + k x ^ { 2 } + \ldots$$
where \(k\) is a rational constant to be found.
A student attempts to substitute \(x = 1\) into both sides of this equation to find an approximate value for \(\sqrt { 3 }\).
State, giving a reason, if the expansion is valid for this value of \(x\).