The expression \( X = \frac{1 + \sqrt{5}}{2} \) represents the **golden ratio**, often denoted by the Greek letter \(\phi\) (phi). The golden ratio is an important irrational number that appears frequently in mathematics, art, architecture, and nature.

The approximate decimal value of the golden ratio is:

\[
X = \frac{1 + \sqrt{5}}{2} \approx 1.61803398875
\]

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Here are 5 related questions to consider:
1. What is the significance of the golden ratio in geometry?
2. How is the golden ratio related to the Fibonacci sequence?
3. Can you derive the golden ratio using a quadratic equation?
4. What are some real-world examples of the golden ratio?
5. How does the golden ratio appear in nature and art?

**Tip:** The golden ratio can be derived from the quadratic equation \( x^2 - x - 1 = 0 \). Solving this equation gives the positive root, which is the golden ratio.

Explore the significance of the golden ratio X=(1+√5)/2 in mathematics, art, architecture, and nature. Learn its decimal approximation and its derivation from the quadratic equation. Ideal for students and enthusiasts interested in number theory and geometric principles.

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