Question

if a+1/a=2; find : a4+1/a2 ,a8+1/a4​

Answer 1

$\textbf{Given:}$

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

$\text{This can be written as}$

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

$a^2+1=2a$

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

$(a-1)^2=0$

$\implies\bf\;a=1$

$\text{Now,}$

$a^4+\frac{1}{a^2}$

$=1^4+\frac{1}{1^2}$

$=1+1$

$\implies\boxed{a^4+\frac{1}{a^2}=2}$

$a^8+\frac{1}{a^4}$

$=1^8+\frac{1}{1^4}$

$=1+1$

$\implies\boxed{a^8+\frac{1}{a^4}=2}$

Answer 2

Here is the answer of your question mate!!