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Home » Distance from $(0,0,0)$: - Leaselab

Distance from $(0,0,0)$: - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 The solutions are $ \boxed{2 + \sqrt{7}} $ and $ \boxed{2 - \sqrt{7}} $.

📌 Question: Rationalize the denominator of $ \frac{\sqrt{5}}{\sqrt{3} - \sqrt{2}} $.

📌 Solution: Multiply numerator and denominator by $ \sqrt{3} + \sqrt{2} $:

📌 $$ \frac{\sqrt{5}(\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})} $$

📌 Simplify denominator:

📌 $$ (\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1 $$

📌 Thus, the expression becomes:

📌 $$ \sqrt{5}(\sqrt{3} + \sqrt{2}) = \sqrt{15} + \sqrt{10} $$

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Question: A quantum diagnostic device uses a function $ f(u) = u\sqrt{...
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x^2 \cdot x - 5x^2 + 6x = 0 \Rightarrow x^3 - 5x^2 + 6x = 0
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$ x = 0 \Rightarrow u = 0 $
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The sum of all real, non-negative roots is:
+ 4 + 9 = \boxed{13}

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