The golden ratio rho can be defined by lim n → [infinity] bn = rho , where rho = 1 + 1/rho. solve this equation for rho. (round your answer to four decimal places.)

(rounding to four decimal places)

Step-by-step explanation:

As a clarification note: The Golden Ratio is usually represented by the Greek letter phi () and not by rho letter (). To answer the question, we will use the rho letter.

To solve this equation:

We need first to rearrange its terms and then apply the quadratic formula for it, since the result of such rearrangement is a quadratic equation.

Then, the equation can be multiplied by to both of its sides. The equation remains the same in doing so.

, which is a quadratic equation that can be solved using the well known quadratic formula aforementioned.

A quadratic equation is of the form:

And the formula for solving it has two solutions:

Well, applying it for:

, we have

Then, the first solution is:

The second solution is:

But, the Golden Ratio is a positive number since it is a ratio between positive quantities, thus, the valid solution for the Golden Ratio is the first solution. The second solution is a negative number.

, which is the exact solution.

Since the question is asking to round this answer to four decimal places, then we have:

Therefore

or

(rounding to four decimal places).

x + 4/7

step-by-step explanation:

use cymath