Explanation

(a)
Let $y = \sqrt{42 + \sqrt{42 + \sqrt{42} + \ldots}}$
$\Rightarrow \ \ \ y = \sqrt{42 + y}$
On squaring both sides, we get
$y^{2} = 42 + y$
$\Rightarrow y^{2} - y - 42 = 0$
$\Rightarrow (y - 7)(y + 6) = 0$
$\Rightarrow \ \ y = 7,\ 6$
Since, $y = - 6$ does not satisfy the given equation
$\therefore\ \$ The required solution is $y = 7$