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Math Help - System of Inequalities

  1. #1
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    System of Inequalities

    t^2 - k^2 < 6
    t + k > 4
    t > k

    Both t and k are positive integers. What is the value of t? Multiple choice: 1, 2, 3, 4, or 5

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    I'm confused by the way this is worded... It seems to say that there is only one value of t which satisfies this system. But if I graph this, I get an entire region, not just one value? In fact, it would seem if I graph this I get no overlap of shaded regions. I don't get it.

    I guess one way is to just start trying numbers, but there must be a better way?
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  2. #2
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    t can't be 1 or 2 by the 2nd and 3rd inequality. Also, k > 4-t which tell us t can't be 4 so t is 1, 2, or 3 but we know t isn't 1 or 2.
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  3. #3
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    Quote Originally Posted by Reiner View Post
    t^2 - k^2 < 6 [1]
    t + k > 4 [2]
    t > k [3]
    [1] (t + k)(t - k) < 6 [1A]
    [2] t + k = 5 minimum [2A]

    Substitute [2A] in [1A]:
    5(t - k) < 6
    So t - k < 2

    [3] t > k
    So t = 3, k = 2
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