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3rd Time Trial, National Road Championships - Redraw

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: A renewable energy system’s efficiency is modeled by the equation $ \frac{a + 2b}{a - 2b} + \frac{a - 2b}{a + 2b} = 2 $. Find $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $.

📌 Solution: Let $ x = \frac{a + 2b}{a - 2b} $. Then the equation becomes:

📌 x + \frac{1}{x} = 2

📌 Multiplying both sides by $ x $:

📌 x^2 + 1 = 2x \Rightarrow x^2 - 2x + 1 = 0 \Rightarrow (x - 1)^2 = 0 \Rightarrow x = 1

📌 So $ \frac{a + 2b}{a - 2b} = 1 \Rightarrow a + 2b = a - 2b \Rightarrow 4b = 0 \Rightarrow b = 0 $

📌 Now compute $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $. Since $ b = 0 $, this becomes:

📌 \frac{a^2}{a^2} = \boxed{1}

🔥 Popular Posts

= 128 + 64 + 0 + 16 + 0 + 4 + 2 + 0 = 214
Answer:** \(\boxed{214}\)
Data Analysis – Average Rainfall Trend
A climate study in Oregon records monthly rainfall (in mm):
Sep: 110, Oct: 95, Nov: 78, Dec: 68
Compute the average monthly rainfall and determine if it decreased by...
Average = \(\frac{110 + 95 + 78 + 68}{4} = \frac{351}{4} = 87.75\) mm
Decrease from September:
\div 110 = 0.7955 \Rightarrow 79.55\%
79.55% ≥ 15% → decrease is significant.

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