Question

If the sum of a number and its reciprocal is 2, what is the difference between them?

Answer 1

Let the number be 'a'.
a + $\frac{1}{a}$ = 2

Squaring both sides,
(a + $\frac{1}{a}$)${}^2$ = 4
a${}^2$ + $\frac{1}{a^2}$ + 2 = 4
a${}^2$ + $\frac{1}{a^2}$ = 4 - 2 = 2
Now, (a - $\frac{1}{a}$)${}^2$ = a${}^2$ + $\frac{1}{a^2}$ - 2 = 2 - 2 = 0
So, a - $\frac{1}{a}$ = 0.