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early signs of schizophrenia - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 For $ 2 < x < rac{11}{3} $, say $ x = 3 $: numerator $ -9 + 11 = 2 > 0 $, denominator $ 1 > 0 $ â positive.

📌 For $ x > rac{11}{3} $, say $ x = 4 $: numerator $ -12 + 11 = -1 < 0 $, denominator $ 2 > 0 $ â negative.

📌 We want where the expression is **less than 0**, so the solution is where it is negative: $ (-\infty, 2) \cup \left(rac{11}{3}, \infty

📌 x \in (-\infty, 2) \cup \left(rac{11}{3}, \infty

📌 oxed{(-\infty, 2) \cup \left(rac{11}{3}, \infty

📌 Question: Let $ a, b, c $ be real numbers such that $ a + b + c = 0 $. Prove that $ a^3 + b^3 + c^3 = 3abc $.

📌 Solution: We use the well-known algebraic identity:

📌 a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

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