-/+ Root Solutions

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  1. pleasedtobeatyou's Avatar
    • Respected Member
    • Posts: 225
    -/+ Root Solutions
    \sqrt{10}cos(x-a)=2

    The mark scheme lists the only solutions when 2 is divided by positive root 10

    Why wouldn't the solutions where 2 is divided by negative root 10 be acceptable?
  2. raheem94's Avatar
    • TSR Demigod
    • Posts: 5,512
    Re: -/+ Root Solutions
    (Original post by pleasedtobeatyou)
    \sqrt{10}cos(x-a)=2

    The mark scheme lists the only solutions when 2 is divided by positive root 10

    Why wouldn't the solutions where 2 is divided by negative root 10 be acceptable?
     \sqrt4 = 2 \not= \pm 2

    The value obtained from the square root is always taken as positive.
  3. njl94's Avatar
    • New Member
    • Location: UK
    • Posts: 24
    Re: -/+ Root Solutions
    maybe there is some limitation on x, like 0\leq x\leq \pi
  4. pleasedtobeatyou's Avatar
    • Respected Member
    • Posts: 225
    Re: -/+ Root Solutions
    This is from Core 4 but in some Core 3 questions for example,

    tan^2x = 6

    There's a need to find the solutions for -root6 and +root6
  5. pleasedtobeatyou's Avatar
    • Respected Member
    • Posts: 225
    Re: -/+ Root Solutions
    (Original post by njl94)
    maybe there is some limitation on x, like 0\leq x\leq \pi
    Nope, the solutions for the negative root would also be acceptable
  6. raheem94's Avatar
    • TSR Demigod
    • Posts: 5,512
    Re: -/+ Root Solutions
    (Original post by pleasedtobeatyou)
    This is from Core 4 but in some Core 3 questions for example,

    tan^2x = 6

    There's a need to find the solutions for -root6 and +root6
     \tan^2 x  = 6 \implies \tan x = \pm \sqrt{6}

    It is the same as  x^2 = 4 \implies x  = \pm \sqrt4 = \pm 2

    But  x = \sqrt4 = 2 \not= \pm \sqrt2
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