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Home » We apply the Chinese Remainder Theorem step by step. - jntua results

We apply the Chinese Remainder Theorem step by step. - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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w^2 \cdot w - 8w^2 + 9w - 18 = 0 \Rightarrow w^3 - 8w^2 + 9w - 18 = 0.
Wir suchen die Summe der Wurzeln der ursprünglichen Gleichung in \( v...
w_1 + w_2 + w_3 = 8, \quad w_1w_2 + w_2w_3 + w_3w_1 = 9, \quad w_1w_2w...
Wir wollen \( \sum v_i = \sum w_i^2 \) berechnen. Mit der Identität:
\sum w_i^2 = (w_1 + w_2 + w_3)^2 - 2(w_1w_2 + w_2w_3 + w_3w_1),
setzen wir die Vieta’schen Werte ein:
\sum w_i^2 = 8^2 - 2 \cdot 9 = 64 - 18 = 46.
Wir müssen überprüfen, ob alle Wurzeln \( w_i \) reell und positiv sin...
\( f'(w) = 3w^2 - 16w + 9 \). Diskriminante: \( 256 - 108 = 148 > 0 \)...
\( w = \frac{16 \pm \sqrt{148}}{6} = \frac{16 \pm 2\sqrt{37}}{6} = \fr...

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