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Math Help - Equation

  1. #1
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    Equation

    Is there any real x that solves \sqrt{x^4+x+2}=\sqrt[3]{x^5+8x+1}?

    (I checked with Wolfram Mathematica and got 2 real (and 2 complex) roots.)

    Of course I only have to show that there are real root(s) and don't have to find them.
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  2. #2
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    f(x) = \sqrt{x^4 + x + 2} - \sqrt[3]{x^5 + 8x + 1}

    consider the signs of f(0) and f(1).
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by skeeter View Post
    f(x) = \sqrt{x^4 + x + 2} - \sqrt[3]{x^5 + 8x + 1}

    consider the signs of f(0) and f(1).
    And also the sign change from f(1) to f(2)
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