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Home » Incredibles Syndrome Explained: The Hidden Epidemic That Could Change Everything! - Parker Core Knowledge

Incredibles Syndrome Explained: The Hidden Epidemic That Could Change Everything! - Parker Core Knowledge

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 We seek integer \( x, y \) such that:

📌 \frac{x^2}{16} + \frac{y^2}{9} = 1, \quad |x| \leq 4, \quad |y| \leq 3

📌 Multiply both sides by \( 144 = 16 \cdot 9 \):

📌 \cdot \left( \frac{x^2}{16} + \frac{y^2}{9} \right) = 9x^2 + 16y^2 = 144

📌 So we solve \( 9x^2 + 16y^2 = 144 \) in integers with \( |x| \leq 4 \), \( |y| \leq 3 \).

📌 We try all integer \( x \) from \( -4 \) to \( 4 \), compute \( 9x^2 \), then \( 16y^2 = 144 - 9x^2 \), so \( y^2 = \frac{144 - 9x^2}{16} \), must be a perfect square and integer.

📌 \( x = 0 \): \( y^2 = \frac{144}{16} = 9 \) → \( y = \pm 3 \) → valid

📌 \( x = \pm 1 \): \( 9(1) = 9 \), \( 144 - 9 = 135 \), \( y^2 = 135/16 \) → not integer

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