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Home » $$ 12a + 8b = 156 $$ - Dyverse

$$ 12a + 8b = 156 $$ - Dyverse

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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We want positive ratio. Try $ y = \frac{-7 + \sqrt{7}}{9} \approx \fra...
Wait — the original assumption about ordering may be wrong. Try symmet...
2a^2 + 18d^2 = 16a^2 \Rightarrow 18d^2 = 14a^2 \Rightarrow \frac{d^2}{...
Third term: $ a + d $, first: $ a - 3d $. Ratio:
\frac{a + d}{a - 3d} = \frac{1 + \frac{d}{a}}{1 - 3\frac{d}{a}}.
Let $ x = \frac{d}{a} $, $ x^2 = \frac{7}{9} \Rightarrow x = \pm \frac...
\frac{1 + \frac{\sqrt{7}}{3}}{1 - \sqrt{7}} = \frac{\frac{3 + \sqrt{7}...
Numerator: $ (3 + \sqrt{7})(1 + \sqrt{7}) = 3 + 3\sqrt{7} + \sqrt{7} +...
Denominator: $ 3(1 - 7) = 3(-6) = -18 $.
So ratio: $ \frac{10 + 4\sqrt{7}}{-18} = -\frac{5 + 2\sqrt{7}}{9} $.

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