A soma dos quadrados de dois números positivos consecutivos é 41.Calcule o maior dos números

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12-11-2016
Mathematics

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A soma dos quadrados de dois números positivos consecutivos é 41.Calcule o maior dos números

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Aliwohaish12 Aliwohaish12 · Answer 1 · 2016-11-12T18:47:28+01:00

Aliwohaish12 Aliwohaish12

12-11-2016

x2+ y2 = 41 [1] x+ y = 9 --> x = 9- y [2] Substituindo [2] em [1], (9- y)^2+ y2 = 81- 18y+ 2y^2 = 41 2y^2- 18y+ 40 = 0 (y- 5)(2y- 8) = 0 y1 = 5 y2 = 4 Substituindo em y1 e y2 em [2], x1 = 4 x2 = 5 Resposta: 4 e 5 (ou 5 e 4, que dá na mesma)

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