What number differs from its reciprocal by 1?
(What is the significance of that number?)
Solution to Problem:
The answer is 1.61803...
Other possibilities are -1.61803..., or .61803...,
or - .61803...
These are the decimal approximations for
(1 + sqrt(5))/2 and
(1 - sqrt(5))/2 or
(-1 + sqrt(5))/2 and
(-1 + sqrt(5))/2
This number is called THE GOLDEN RATIO.
To solve for this number,
let n = the number and 1/n = its reciprocal.
Then n - 1/n = 1 (or 1/n - n = 1)
Multiplying by n, n^2 - 1 = n
So n^2 - n - 1 = 0
Using the quadratic formula,
n = (1 + sqrt(5)) / 2
and n = (1 - sqrt(5)) / 2
Correctly solved by:
| 1. Kirstine Wynn | Winchester, VA |
| 2. Matthias | Switzerland |