Explanation

(c) Let $x$ be the equivalent resistance of entire network between A and B. Hence, we have
$R_{AB} = 1 +$ resistance of parallel combination of 1$\Omega$ and $x\Omega$
$\therefore\ \ \ \ \ \ \ \ \ R_{AB} = 1 + \frac{x}{1 + x}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 1 + \frac{x}{1 + x}$
$\Longrightarrow \ \ x + x^{2} = 1 + x + x$
$\Longrightarrow x^{2} - x - 1 = 0$
$\Longrightarrow \ \ x = \frac{1 + \sqrt{1 + 4}}{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1 + \sqrt{5}}{2}\Omega$