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1 gallon water jug with handle - Redraw

📅 May 4, 2026 👤 scraface

May 04, 2026

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\[ a^2 - b^2 = 0 \quad \text{(1)} \]
\[ 2ab = -2 \quad \text{(2)} \]
From (1): \( a^2 = b^2 \Rightarrow a = b \) or \( a = -b \)
Try \( a = b \):
Then (2): \( 2a^2 = -2 \Rightarrow a^2 = -1 \) — not possible in reals...
Try \( a = -b \):
Let \( b = -a \), then (2): \( 2a(-a) = -2a^2 = -2 \Rightarrow a^2 = 1...
If \( a = 1 \), \( b = -1 \), then \( (a + bi)^2 = (1 - i)^2 = 1 - 2i...
If \( a = -1 \), \( b = 1 \), \( (-1 + i)^2 = 1 - 2i + i^2 = -2i \) ✅
So the square roots are \( 1 - i \) and \( -1 + i \)

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