Question

if a≠0 and a-1÷a =3 find a²+1÷a²​

Answer 1

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Answer 2

$\rm{a - \frac{1}{a} = 3}$

$\rm{\underline{squaring on both sides}}$

$\rm{ {(a - \frac{1}{ a } )}^{2} = {a}^{2} + \frac{1}{ {a}^{2} } - 2}$

$\rm{ {3}^{2} = {a}^{2} + \frac{1}{ {a}^{2} } - 2}$

$\rm{9 = {a}^{2} + \frac{1}{ {a}^{2} } - 2}$

$\rm{{a}^{2} + \frac{1}{ {a}^{2} } = 9 + 2}$

$\fbox{ \rm{{a}^{2} + \frac{1}{ {a}^{2} } =11}}$