e)
x^2+1/x^2=5
(x+1/x)^2=x^2+2*x*1/x+1/x^2=x^2+1/x^2+2
Observam astfel ca putem scrie prima relatie astfel:
x^2+1/x^2+2-2=5
(x+1/x)^2=7
x+1/x= plus minus√7
(x-1/x)^2=x^2+1/x^2-2x*1/x=x^2+1/x^2-2
Asa ca puteam scrie prima relatie astfel:
x^2-2+1/x^2+2=5
(x-1/x)^2+2=5
(x-1/x)^2=3
x-1/x=plus minus√3
f)
x+1/x=2 |^2
(x+1/x)^2=4
x^2+1/x^2+2=4
x^2+1/x^2=2
x^2+1/x^2=2 |^2
(x^2+1/x^2)=4
x^4+1/x^4+2=4
x^4+1/x^4=2
