Question

a-1/a=8 find 1) a+1/a. 2)a^2-1/a^2

Answer 1

hope it helps you....

Answer 2

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

1) $\sf{{(a + \frac{1}{a})}^{2} - {(a - \frac{1}{a}) }^{2} = 4}$

$\sf{{(a + \frac{1}{a})}^{2} - {8}^{2} = 4}$

$\sf{{(a + \frac{1}{a})}^{2} - 64 = 4}$

$\sf{{(a + \frac{1}{a})}^{2} = 4 + 64}$

$\sf{{(a + \frac{1}{a})}^{2} = 68}$

$\fbox{\bf{a + \frac{1}{a}} = \sqrt{68} }$

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

$\sf{( \sqrt{68})(8) = {a}^{2} - \frac{1}{ {a}^{2} }}$

$\fbox{ \bf{{a}^{2} - \frac{1}{ {a}^{2} } = 8 \sqrt{68} }}$