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Home » \(r_1r_2 = 6\) (product of roots) - Malaeb

\(r_1r_2 = 6\) (product of roots) - Malaeb

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Total distance = 500 km (500 back and forth).

📌 Total time = 3 + 2 = 5 hours.

📌 Average speed = \( \frac{500}{5} = 100 \) km/h.

📌 Solve for \( x \): \( 3^{2x+1} = 81 \cdot 3^{x-1} \).

📌 Express 81 as \( 3^4 \), so equation becomes:

📌 \( 3^{2x+1} = 3^4 \cdot 3^{x-1} = 3^{4 + x - 1} = 3^{x+3} \).

📌 Since bases are equal, set exponents equal:

📌 \( 2x + 1 = x + 3 \) → \( 2x - x = 3 - 1 \) → \( x = 2 \).

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But let's use a corrected version with exact fit.
Wait — in practice, such problems use rounding.
But for math olympiad, precise decimal acceptable.
Alternatively, change question to avoid decimal gesture issue.
But instruction is to generate difficult one.
Recompute sum:
+ 1.1 = 2.1
+1.21 = 3.31
+1.331 = 4.641
+1.4641 = 6.1051 — correct.

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