Question

if a+1/a=m and a≠0 find the value of a-1/a in terms of m

Answer 1

$use \: \: the \: \: identity \\ {(a + \frac{1}{a}) }^{2} - {(a - \frac{1}{a}) }^{2} = 4 \\ therefore \\ {(a - \frac{1}{a}) }^{2} = {(a + \frac{1}{a}) }^{2} - 4 \\ = {m}^{2} - 4 \\ thus \: \: a - \frac{1}{a} = \sqrt{ {m}^{2} - 4}$
${a}^{2} - \frac{1}{ {a}^{2} } = (a + \frac{1}{a} )(a - \frac{1}{a} ) \\ = m \sqrt{ {m}^{2} - 4}$