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Home » Utiliser les propriétés des logarithmes : \( \log_2 x + \log_2 4 = \log_2 (4x) = 5 \). - Dachbleche24

Utiliser les propriétés des logarithmes : \( \log_2 x + \log_2 4 = \log_2 (4x) = 5 \). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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\frac{a}{b} + \frac{b}{a} = 5
Let $ x = \frac{a}{b} $. Then $ \frac{b}{a} = \frac{1}{x} $, so:
x + \frac{1}{x} = 5
We want to compute:
\frac{a^2 + b^2}{a^2 - b^2} + \frac{a^2 - b^2}{a^2 + b^2}
Note that:
a^2 + b^2 = b^2(x^2 + 1), \quad a^2 - b^2 = b^2(x^2 - 1)
So the expression becomes:
\frac{b^2(x^2 + 1)}{b^2(x^2 - 1)} + \frac{b^2(x^2 - 1)}{b^2(x^2 + 1)}...
Let $ y = \frac{x^2 + 1}{x^2 - 1} $, then the expression becomes:

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