Wednesday, April 7, 2010

Solución 012

Factorizamos la ecuación
::: 2sen3x + sen2x - 2senx -1 = 0; 0 ≤ x ≤ 2π
::: sen2x(2senx + 1) - (2senx + 1) = 0
::: (sen2x - 1)(2senx + 1) = 0
::: (senx - 1)(senx + 1)(2senx + 1) = 0

::: Para senx = 1 → x = π/2
::: Para senx = -1 → x = 3π/2
::: Para senx = (-1/2) → x = 7π/6; x = 11π/6

Sumando
::: π/2 + 3π/2 + 7π/6 + 11π/6 = 5π

VOLVER A LA PREGUNTA ::: UNI 2010-I: MATEMATICA

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