Question

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

Answer 1

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