lean_workbook_plus_6407

now if $a=0$ then it is obviously true, so let $|a|>0$ then we have to show $|1+\frac{b}{a}|+2|1-\frac{b}{a}|\ge 2$ or $|1+k|+2|1-k|\ge 2, \forall k\in\mathbb{R}$