Question

if a + 1/a = 1 then the value of a^2 - a + 1/a^2 + a + 1

Answer 1

Answer:

$a + \frac{1}{a} = 1 \\ taking \: square \: on \: both \: side \\ {(a + \frac{1}{a} )}^{2} = {1}^{2} \\ {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 1 \\ {a}^{2} + \frac{1}{ {a}^{2} } = - 1 \\adding \: and \: subtracting \: a \: to \: left \: hnd \: side \\ {a}^{2} - a + \frac{1}{ {a}^{2} } + a = - 1 \\ adding \: 1 \: to \: both \: side \\ {a}^{2} - a + \frac{1}{ {a}^{2} } + a + 1 = - 1 + 1 \\ {a}^{2} - a + \frac{1}{ {a}^{2} } + a + 1 = 0$