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The golden ratio is a solution to a quadratic equation.

a. Find the precise value for Φ by solving Φ2 − Φ − 1 = 0.

b. Which method of solving a quadratic equation did you use? Explain your reasoning.

c. What type of number is Φ? Why can it only be approximated by a decimal value?

Respuesta :

oscar236

Answer:

Below.

Step-by-step explanation:

a.    Φ^2 − Φ − 1 = 0

Φ2 − Φ = 1

(Φ - 0.5)^2 - 0.25 = 1

(Φ - 0.5)^2 = 1.25

Φ - 0.5 = √(1.25)      (We only take the positive root).

Φ  = 0.5 + √(1.25)

b. I used Completing the square.

c.  Φ is irrational That is it cannot be represented as a fraction a/b and because of this it can only be approximated by a decimal.

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