This is gold

Algebra Level 2

What fraction greater than zero equals one more than its reciprocal? State in decimal form and round to the nearest thousandth.

The answer is 1.61803.

4 solutions

Feathery Studio
Apr 29, 2015

Since 1 divided by any number is its reciprocal,

$x=\frac{1}{x} + 1$

$x^{2}=x+1$

$x^{2}-x-1=0$

By quadratic formula,

$x=\frac{1 \pm \sqrt{5}}{2}$

Because we do not consider the negative root of this equation,

$x=\frac{1 + \sqrt{5}}{2} \approx \boxed{1.618}$

Moderator note:

Yes. Correct. I'm added that the answer must be positive, else we could have $\frac {1-\sqrt5}{2}$ as another answer. Note that this constant is known as the "Golden ratio". It is extensively used in architecture, and appears very often in nature. It is also known to be the limit of ratio of successive Fibonacci numbers, $\phi = \displaystyle \lim_{n \to\infty} \frac {F_{n+1}}{F_n}=\frac{1+\sqrt5}{2}\approx1.618$ .

Thank you This really helps

A S - 6 years, 1 month ago

Karan Pedja
May 1, 2015

Is $\sqrt{5}$ cosidered a fraction?

Shakil Md Resvy
Apr 30, 2015

For the fraction to be greater than zero,x> y(should be), so assume x=any number, I took 16.Then 16/y=(y/16)+1.Ignoring the negative value as x/y> 0, so y~9.889 to nearest thousandth, hence x/y=16/9.889~1.618😊

A S
Apr 28, 2015

This problem is so hard that i need everyones help to teach me how they got the answer

Moderator note:

It's easy to set up an equation. Give it a try!

I know how to set it X/Y=(Y+X) /X But then what do i do?

A S - 6 years, 1 month ago

This is gold

The answer is 1.61803.

4 solutions

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