Question

if a+1/a =2 find a^2+1/a^2​

Answer 1

Step-by-step explanation:

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

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

$= {a}^{2} + 1 = 2a$

$= {a}^{2} - 2a + 1 = 0$

$= {a}^{2} - a - a + 1 = 0$

$= a(a - 1) - 1(a - 1) = 0$

$= (a - 1)(a - 1) = 0$

$= a - 1 = 0$

$= a = 1$

$so \\ \frac{1}{a} = 1$

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