Question

if a-1/a=10, find i)a+1/a ii)a^2-1/a^2

Answer 1

Answer:

$1. \: \sqrt{104} \\ 2. \: 10 \sqrt{104}$

Step-by-step explanation:

$a - \frac{1}{a} = 10 \\ {(a - \frac{1}{a})}^{2} = {10}^{2} \\ {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 100 \\ {a}^{2} + \frac{1}{ {a}^{2} } = 102 \\ {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 104 \\ {(a + \frac{1}{a})}^{2} = {104} \\ a + \frac{1}{a} = \sqrt{104}$

$(a + \frac{1}{a} )(a - \frac{1}{a} ) = 10 \times \sqrt{104} \\ ( {a}^{2} - { \frac{1}{a} }^{2} ) = 10 \sqrt{104}$

Answer 2

Answer:

1.

$\sqrt{104}$

2.

$10 \sqrt{104}$