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e n j a m b m e n t - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 $ xv + yu = -2 $.

📌 From $ u = 2 - x $, $ v = 4 - y $. Substitute:

📌 $ x(2 - x) - y(4 - y) = 13 \Rightarrow 2x - x^2 - 4y + y^2 = 13 $,

📌 $ x(4 - y) + y(2 - x) = 4x - xy + 2y - xy = 4x + 2y - 2xy = -2 $.

📌 First equation: $ -x^2 + y^2 + 2x - 4y = 13 $.

📌 Second equation: $ 4x + 2y - 2xy = -2 \Rightarrow 2x + y - xy = -1 $.

📌 Let $ y = -1 - 2x + xy $ â circular. Solve second: $ 4x + 2y = 2xy - 2 $. Divide by 2: $ 2x + y = xy - 1 $.

📌 Let $ y = x - 1 - rac{1}{x} $ â not helpful. Try numerical values. From $ z + w = 2 + 4i $, $ zw = 13 - 2i $, $ z $ and $ w $ are roots of $ t^2 - (2 + 4i)t + (13 - 2i) = 0 $. Compute discriminant $ D = (2 + 4i)^2 - 4(13 - 2i) = 4 + 16i - 16 - 52 + 8i = -64 + 24i $. Let $ \sqrt{D} = a + bi $, then $ (a + bi)^2 = a^2 - b^2 + 2abi = -64 + 24i $. So:

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