Question

if x^5+1/x^5=123 , x+1/x=?​

Answer 1

Step-by-step explanation:

(x+1/x)^5=x^5+1/x^5+5(x^3+1/x^3)+10(x+1/x)

=123+5{(x+1/x)^3-3(x+1/x)}+10(x+1/x)

=123+5(x+1/x)^3-5(x+1/x)

(x+1/x)^5-5(x+1/x)^3+5(x+1/x)-123=0

let x+1/x=z

z^5-5z^3+5z-123=0

(z-3)(z^4+3z^3+4z^2+12z+41)=0

z=3

x+1/x=3