Explanation

(b)
Since, $\beta\beta\gamma\delta = 1$ …(i)
As we know, AM$\geq$GM
$\Rightarrow \frac{1 + \alpha}{2} \geq \sqrt{\alpha} \Rightarrow 1 + \alpha \geq 2\sqrt{\alpha}$ …..(ii)
Similarly, $1 + \beta \geq 2\sqrt{\beta\ \ \ \ \ }\ \ \ \ \ldots(iii)$
$1 + \gamma \geq 2\sqrt{\gamma}$ …(iv)
And $1 + \delta \geq 2\sqrt{\delta\ }\ \ \ \ \ \ \ldots(v)$
On multiplying Eqs. (ii), (iii), (iv) and (v), we get
$(1 + \alpha)(1 + \beta)(1 + \gamma)(1 + \delta) \geq 16\sqrt{\alpha\beta\gamma\delta}$
Least value of $(1 + \alpha)(1 + \beta)(1 + \gamma)(1 + \delta) \geq 16$