Then $ x^2 \approx 22.96 $, so:
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- Let’s try plugging values:
- Let $ x = \frac{5 + \sqrt{21}}{2} $, then $ x + \frac{1}{x} = 5 $. Compute numerically:
- x = \frac{5 + \sqrt{21}}{2} \approx \frac{5 + 4.583}{2} = \frac{9.583}{2} \approx 4.7915
- \frac{x^2 + 1}{x^2 - 1} + \frac{x^2 - 1}{x^2 + 1} \approx \frac{23.96}{21.96} + \frac{21.96}{23.96} \approx 1.093 + 0.917 = 2
- \boxed{2}
- Final Answer:
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