Question

If a+1/a = 2 then find a^2+1/a^2 and a-1/a

Answer 1

Answer:

2 and 0

Step-by-step explanation:

$a + \frac{1}{a} = 2$

Squaring on both sides,

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

Also,

${a}^{2} + \frac{1}{ {a}^{2} } = 2 \\ {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 0 \\ {(a - \frac{1}{a} )}^{2} = 0 \\ a - \frac{1}{a} = 0$

Thank you