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how do you build a furnace on minecraft - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Solution: To minimize

📌 under the constraint $ x + y + z = 1 $, we apply the **Cauchy-Schwarz Inequality** in the following form:

📌 Equality occurs when $ \frac{x}{y} = \frac{y}{z} = \frac{z}{x} $, which implies $ x = y = z $. Since $ x + y + z = 1 $, we have $ x = y = z = \frac{1}{3} $.

📌 \frac{(1/3)^2}{1/3} + \frac{(1/3)^2}{1/3} + \frac{(1/3)^2}{1/3} = 3 \cdot \frac{1/9}{1/3} = 3 \cdot \frac{1}{3} = 1

📌 Therefore, the minimum value is $ \boxed{1} $.

📌 Question: Compute the sum of the roots of the equation

📌 u\sqrt{u} - 6u + 7\sqrt{u} - 12 = 0,

📌 given that all roots are real and non-negative.

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And $ d = 2 $
p(x) = \frac{4}{3}x^3 - 2x^2 + \frac{11}{3}x + 2
Thus, the remainder when $ p(x) $ is divided by $ x^4 - 1 $ is simply...
\boxed{\frac{4}{3}x^3 - 2x^2 + \frac{11}{3}x + 2}
Question: Let $ a $ and $ b $ be complex numbers such that $ a + b = 4...
We know $ a + b = 4 $, and
a^2 + b^2 = (a + b)^2 - 2ab = 16 - 2ab = 10 \Rightarrow 2ab = 6 \Right...
a^3 + b^3 = 4^3 - 3 \cdot 3 \cdot 4 = 64 - 36 = \boxed{28}
Question: Let $ x, y, z $ be positive real numbers such that $ x + y +...
Solution: We apply the **Cauchy-Schwarz inequality** in the Engel form...

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