Question

Sabe-se que (x+1/x)2= 10. Qual o valor de x2+1/x2?

Answer 1

((x+1)/x).2 =10
(x+1)/x = 10/2
x+1 = 5.x
1= 5x -x
4x=1
x= 1/4
substituindo...
(2x+1)/2x=
(2.1/4 +1)/ (2.1/4)=
(2/4 +1)/ (2/4)=
(1/2 +1)/ (1/2)=
(3/2) / (1/2)=
(3/2).(2/1)=
3