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9 September, 14:50

Solve 2cos^2x + cosx - 1 = 0 for x over the interval [0, 2 π).

a.π and π/3

b.π, π/3, and 5π/3

c. 1 and 2π/3

d. 1, 2π/3, and 4π/3

e. 1, π/3, and 5π/3

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Answers (1)
  1. 9 September, 15:31
    0
    Let cos x = a, then

    2a^2 + a - 1 = 0,

    solving the quadratic equation, we have:

    a = 0.5 or - 1.

    i. e. cos x = 0.5 or cos x = - 1

    for cos x = 0.5,

    x = pi/3, 2pi - pi/3 = pi/3, 5pi/3

    for cos x = - 1,

    x = pi

    therefore, x = pi, pi/3, 5pi/3

    Answer: B
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