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Home » \( 64a + 16b + 4c + d = 85 \) - Groen Casting

\( 64a + 16b + 4c + d = 85 \) - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Solution: Let \( a = 2x \), \( b = y \), so the equation becomes:
rac{a + b}{a - b} + rac{a - b}{a + b} = 3
Let \( u = rac{a + b}{a - b} \), then the expression is \( u + rac{1...
u^2 + 1 = 3u \Rightarrow u^2 - 3u + 1 = 0
So \( rac{a + b}{a - b} = rac{3 \pm \sqrt{5}}{2} \). Letâs take on...
rac{a + b}{a - b} = rac{3 + \sqrt{5}}{2}
2(a + b) = (3 + \sqrt{5})(a - b)
2a + 2b = (3 + \sqrt{5})a - (3 + \sqrt{5})b
2a - (3 + \sqrt{5})a + 2b + (3 + \sqrt{5})b = 0
\Rightarrow a(-1 - \sqrt{5}) + b(5 + \sqrt{5}) = 0

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