O polinômio P é tal que P(x) + x.P(2-x)= x^2 +3 A) Determine P(2) B) Mostre que o grau de P é 1.... Pergunta de ideia deDani76561

Dani76561 @Dani76561

December 2019 1 121 Report

O polinômio P é tal que P(x) + x.P(2-x)= x^2 +3
A) Determine P(2)
B) Mostre que o grau de P é 1

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JK1994

Verified answer

A)
$P(0)+0.P(2-0) = 0^2+3 \\ P(0) = 3 \\ P(2)+x.P(2-2) = 2^2+3 \\ P(2)+2.P(0) = 4+3 \\ P(2)+2.3 = 7 \\ P(2)+6 = 7 \\ P(2) = 7-6 \\ P(2) = 1$

b)
$P(2-x) = y \\ P(-x) = y-2 \\ P(x) = 2-y \\ P(2-x) = 2-P(x) \\ P(x)+x.(2-P(x)) = x^2+3 \\ P(x)+2x-x.P(x) = x^2+3 \\ (1-x).P(x) = x^2-2x+3 \\ P(x) = \frac{x^2-2x+3}{1-x} \\ P(x) = 1-x+\frac{2}{1-x}$

Espero ter ajudado.

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