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Thread: Find the largest real solution

  1. March 6th 2010, 07:46 AM #1
    nandokommando
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    Find the largest real solution

    The largest real solution for x^2/3 - 5x^1/3 + 4 = 0 would be x =

    For this one I only got two solutions, 64 and 1. I thought 64 was the correct answer but apparently I got something wrong. The real answer is 8, does anyone know what I did wrong here?
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  2. March 6th 2010, 08:21 AM #2
    VonNemo19
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    Quote Originally Posted by nandokommando View Post
    The largest real solution for x^2/3 - 5x^1/3 + 4 = 0 would be x =

    For this one I only got two solutions, 64 and 1. I thought 64 was the correct answer but apparently I got something wrong. The real answer is 8, does anyone know what I did wrong here?
    Let u=x^{1/3}, then we have

    u^2-5u+4=0

    (u-4)(u-1)=0\Rightarrow{u}=1,4\Rightarrow{x}=1,64.

    Your answer is correct.
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