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15 May, 23:48

P and q are complex numbers such that |p|=3/4x+2, |q|=2x+1, and |p+q|=2/3x-2. On what interval must x fall on?

Answer choices:

a. (-infinity, - 13/5]

b.[3, infinity)

c.[-8/3,-13/5]

d.[-8/3, - 1/2]

+3
Answers (1)
  1. 16 May, 00:22
    0
    Answer: B

    ( - 3, infinity)

    Step-by-step explanation:

    Given that

    |p| = 3/4x+2

    |q| = 2x+1

    |p+q| = 2/3x-2

    |p| + |q| = |p+q|

    That is

    3/4x+2 + 2x+1 = 2/3x-2

    (3x + 8) / 4 + 2x + 1 = (2x - 6) / 3

    (3x + 8 + 8x + 4) / 4 = (2x - 6) / 3

    Cross multiply

    9x + 24 + 24x + 12 = 8x - 24

    Collect the like terms

    33x + 36 = 8x - 24

    33x - 8x = - 24 - 36

    25x = - 60

    X = - 60/25

    X = - 2.4

    X should fall on the interval of

    (-3, infinity)
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