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Home » Second sum ($k = 4$ to $8$): - Midis

Second sum ($k = 4$ to $8$): - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📝 Recent Posts

x^4 + 1 = x^4 + \frac{1}{x^4} \cdot x^4 = x^4 + \frac{x^4}{x^4} = x^4...
Instead, observe:
\frac{x^2 + 1}{x^2 - 1} + \frac{x^2 - 1}{x^2 + 1} = y + \frac{1}{y} =...
Let’s compute this directly using the identity:
\frac{a + b}{a - b} + \frac{a - b}{a + b} = \frac{(a + b)^2 + (a - b)^...
\frac{2(x^2 + 1)}{x^2 - 1}
From earlier, $ x + \frac{1}{x} = 5 \Rightarrow x^2 + \frac{1}{x^2} =...
x^2 + 1 = x^2 + \frac{x^2}{x^2} = x^2 + 1 \Rightarrow \text{Try direct...
Let $ x = \frac{a}{b} $, then $ x + \frac{1}{x} = 5 \Rightarrow x^2 +...
x^4 + 1 = x^4 + \frac{1}{x^4} \cdot x^4 = x^4 + 1 \Rightarrow \text{No...

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