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Home » Stop Mining Turbulence—Here’s the Quickest Way to Collect Obsidian! - AssociationVoting

Stop Mining Turbulence—Here’s the Quickest Way to Collect Obsidian! - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Question: If \( x + rac{1}{x} = 5 \), what is the value of \( 2x^2 + rac{2}{x^2} \)?

📌 Solution: Square both sides: \( x^2 + 2 + rac{1}{x^2} = 25 \), so \( x^2 + rac{1}{x^2} = 23 \). Multiply by 2: \( 2x^2 + rac{2}{x^2} = 46 \). oxed{46}

📌 Question: Find the intersection of the lines \( y = 3x + 1 \) and \( y = -2x + 11 \).

📌 Solution: Set \( 3x + 1 = -2x + 11 \). Solve for \( x \): \( 5x = 10 \) â \( x = 2 \). Substitute into \( y = 3(2) + 1 = 7 \). The intersection is \( (2, 7) \). oxed{(2, 7)}

📌 Question: If \( m(m + n) = 24 \) and \( m + n = 8 \), what is the value of \( m \)?

📌 Solution: Substitute \( m + n = 8 \) into the first equation: \( m \cdot 8 = 24 \), so \( m = 3 \). oxed{3}Question: A sequence of six real numbers forms an arithmetic progression. The sum of the first three terms is 12, and the sum of the last three terms is 30. What is the sum of all six terms?

📌 Solution: Let the six terms of the arithmetic progression be $ a - 2d, a - d, a, a + d, a + 2d, a + 3d $.

📌 The sum of the first three terms is:

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