Algebra problem

[yalanand]

If x - (1/x) = 1/2, then what is the value of x^2 + (1/x^2)?

(A) 1/4
(B) 3/4
(C) 5/4
(D) 7/4
(E) 9/4

[piyush_nitt]

If x - (1/x) = 1/2, then what is the value of x^2 + (1/x^2)?

(A) 1/4
(B) 3/4
(C) 5/4
(D) 7/4
(E) 9/4

IMO E

x - (1/x) = 1/2

squaring both sides

x^2+ (1/x)^2 - 2 = 1/4

x^2+ (1/x)^2 = 1/4+2

= 9/4