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Home » From Crayon to Masterpiece: This Hamster Drawing Will Blow Your Mind! - High Altitude Science

From Crayon to Masterpiece: This Hamster Drawing Will Blow Your Mind! - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \frac{2a^2 + 2b^2}{a^2 - b^2} = 3

📌 Factor out 2 in the numerator:

📌 \frac{2(a^2 + b^2)}{a^2 - b^2} = 3

📌 \frac{a^2 + b^2}{a^2 - b^2} = \frac{3}{2}

📌 Question: Let $ g(x^2 + 1) = x^4 + 2x^2 + 2 $. Find $ g(x^2 - 1) $.

📌 g(x^2 + 1) = x^4 + 2x^2 + 2

📌 Let’s express the right-hand side in terms of $ x^2 + 1 $.

📌 Let $ u = x^2 + 1 \Rightarrow x^2 = u - 1 $, so:

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#### 370
A science journalist covers a quantum computing breakthrough: a 64-qub...
2⁸⁰ − 2⁶⁴. But approximate: 2⁸⁰ ≈ (2¹⁰)⁸ ≈ (10³)⁸ = 10²⁴, 2⁶⁴ ≈ 10¹⁉²...
Ratio = 2¹⁶⁰. But compute exponent:
2⁸⁰ = 120892581961462417476233206292340255376, 2⁶⁴ = 18446744073709551...
But for simplicity in format:
difference = 2⁸⁰ − 2⁶⁴ ≈ 2⁸⁰ (since 2⁶⁰ is negligible ratio: 2⁸⁰ / 2⁶⁴...
So compute: 2⁸⁰ − 2⁶⁴ = 116 exerc */
#### 116 Exercises later — correct final:
#### 116

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