Explanation

(a)
Since, $a,\ b$ and $c$ are the sides of a $\mathrm{\Delta}\ ABC$, then
$|a - b| < |c| \Rightarrow a^{2} + b^{2} - 2ab < c^{2}$
Similarly, $b^{2} + c^{2} - 2bc < a^{2},\ \ \ c^{2} + a^{2} - 2ca < b^{2}$
On adding, we get
$\left( a^{2} + b^{2} + c^{2} \right) < 2(ab + bc + ca)$
$\Rightarrow \ \frac{a^{2} + b^{2} + c^{2}}{ab + bc + ca} < 2\ \ \ \ \ \ \ldots..(i)$
Also, $D \geq 0,\ (a + b + c)^{2} - 3\lambda(ab + bc + ca) \geq 0$
$\Rightarrow \ \frac{a^{2} + b^{2} + c^{2}}{ab + bc + ca} > 3\lambda - 2\ \ \ \ \ldots\ldots\ldots(ii)$
From Eqs. (i) and (ii),
$3\lambda - 2 < 2$ $\Rightarrow \lambda < \frac{4}{3}$