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Math Help - Find all the real values of a?

  1. #1
    Super Member fardeen_gen's Avatar
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    Find all the real values of a?

    Find all the real values of a for which a^3 + a^2|a + x| + |a^2x + 1| = 1 has at least 4 integral solutions in x.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by fardeen_gen View Post
    Find all the real values of a for which a^3 + a^2|a + x| + |a^2x + 1| = 1 has at least 4 integral solutions in x.
    Split this into four cases:

    a+x \ge 0,\ a^2x+1 \ge 0

    a+x <0,\ a^2x+1 \ge 0

    a+x \ge 0, \ a^2x+1 <0

    a+x < 0, \ a^2x+1<0

    to give four problems but without absolute values in the equations.

    CB
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