A positive real number is 1 more than its reciprocal. Find the number.

Let the number be x, then

x = 1 + 1/x

x^2 = x + 1

x^2 - x = 1

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

(x - 1/2) ^2 = 5/4

x - 1/2 = + or - 5/4

x = 5/4 + 1/2 or - 5/4 + 1/2

x = 7/4 or x = - 3/4

But x is positive,

Therefore, x = 7/4 = 1.75