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Home » ### 高等055：概率题 - DNSFLEX

### 高等055：概率题 - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \(a_4 = 2a_3 + 3 = 2(13) + 3 = 26 + 3 = 29\)

📌 Therefore, the value of \(a_4\) is:

📌 Question:** In a futuristic navigation system, the position of a spacecraft is given by the expressions \(x(t) = 5t^2 + 3t + 2\) and \(y(t) = 2t^2 + 7t + 1\). Find the value of \(t\) when the spacecraft is at the point where \(x(t) = y(t)\).

📌 To find when \(x(t) = y(t)\), set the expressions equal:

📌 5t^2 + 3t + 2 = 2t^2 + 7t + 1

📌 Subtract \(2t^2 + 7t + 1\) from both sides:

📌 5t^2 + 3t + 2 - 2t^2 - 7t - 1 = 0

📌 3t^2 - 4t + 1 = 0

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\gcd(3^{15} - 1, 3^9 - 1) = 3^3 - 1 = 27 - 1 = 26.
Therefore, the greatest common divisor is $oxed{26}$.**Question:** An...
Solution:** Start with the given equation:
rac{x+y}{x-y} + rac{x-y}{x+y} = 3.
Let \( u = rac{x+y}{x-y} \), so the second term becomes \( rac{1}{u}...
u + rac{1}{u} = 3.
Multiply both sides by \(u\) (assuming \(u
u^2 + 1 = 3u \quad \Rightarrow \quad u^2 - 3u + 1 = 0.
u = rac{3 \pm \sqrt{9 - 4}}{2} = rac{3 \pm \sqrt{5}}{2}.
So \( u = rac{3 + \sqrt{5}}{2} \) or \( u = rac{3 - \sqrt{5}}{2} \).

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