A Beautiful Number

Algebra Level 2

To 3 decimal places, find a positive number which is same as the sum of its inverse & 1


The answer is 1.618.

Moaj Ahmed by Moaj Ahmed , 25, Bangladesh

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2 solutions

Noel Lo
Apr 13, 2015

Golden ratio haha...

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Moaj Ahmed
Jan 14, 2015

given , x = 1 x + 1 x = \frac {1}{x} + 1 => x 2 = 1 + x x^2 = 1 + x => x 2 − x − 1 = 0 x^2 - x - 1 = 0 => x = 1 + 5 2 x = \frac{1+\sqrt5}{2} => x = 1.618033989....... => x = 1.618 ( approximately )

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moaj, I don't get your solution. The problem : find a number whose sum with its inverse, is equal to 1. This we must state as x+1/x = 1. But you started with x = 1/x+1 , which is NOT the same thing ! A. Miller

Tony Miller - 2 years, 6 months ago

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