Question

If a^2+1/a^2=66 then find the value of a-1/a (where a>1)

Answer 1

Answer:

$a - \frac{1}{a} = 8$

Step-by-step explanation:

${a}^{2} + \frac{1}{ {a}^{2} } = 66 \\ \\ {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 64 \\ \\ {(a - \frac{1}{a} )}^{2} = {8}^{2} \\ \\ a - \frac{1}{a} = 8 \: \: \: \: \: \: \: \: \: \: because \: \: a > 1$