Question

$if \frac{a {}^{2} }{b} = c - d \\ then \: prove \: that \frac{ \sqrt{bc - db} }{a} = 1$

Answer 1

$\frac{ {a}^{2} }{b} = c - d \\ \\ {a}^{2} = b(c - d) \\ \\ {a}^{2} = bc - bd \\ \\ a = \pm \sqrt{bc - bd} \\ \\ 1 = \pm \frac{ \sqrt{bc - bd} }{a}$
hence, √(bc - bd)/a = 1 proved

Answer 2

$\text{Given,}\\ \frac{ {a}^{2} }{b} = c - d \\ \\ \Rightarrow{a}^{2} = b(c - d) \\ \\\Rightarrow {a}^{2} = bc - bd \\ \\ \Rightarrow a = \pm \sqrt{bc - bd} \\ \\ \Rightarrow 1 = \pm \frac{ \sqrt{bc - bd} }{a}\\or\\\Rightarrow \boxed{\boxed{\pm \frac{ \sqrt{bc - bd} }{a} = 1}}$