pre-calculus

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solve the following inequality
16(x^2-1) >16x
the solution set is? or there is no solution.

  • pre-calculus -

    This problem can be solved exactly like a quadratic equation would be:

    16(x^2-1) > 16x

    16x^2 - 16 > 16x

    16x^2 - 16x - 16 > 0
    a b c

    You use the quadratic formula:

    x = (-b +/- sqrt(b^2 - 4ac))/2a

  • pre-calculus -

    the problem here is that after having solved the equation, you now know where the graph crosses the x-axis. You want to know where

    16(x^2-1) > 16x
    x^2 - 1 > x
    x^2 - x - 1 > 0

    Now from what you know about parabolas, it should clear that the graph is above the x-axis everywhere except between the roots, which you found using the method described above.

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