SOLUTION: What is the solution set of x²-4x-12>0 and x²-8x+15<0

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Question 1186615: What is the solution set of x²-4x-12>0 and x²-8x+15<0
Answer by ikleyn(52781) About Me  (Show Source):
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What is the solution set of x²-4x-12 > 0 and x²-8x+15 < 0 ?
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First inequaliy  x%5E2-4x-12 > 0  in factored form is

    %28x-6%29%2A%28x%2B2%29 > 0.

Its solution set is the union of these two semi-infinite intervals  (-oo,-2) U (6,oo)  (see the plot below)


    =============)-------|---------------------------(=========

                -2       0                           6



Second inequaliy  x%5E2-8x%2B15 < 0  in factored form is

    %28x-3%29%2A%28x-5%29 > 0.

Its solution set is this interval  (3,5)  (see the plot below)


    ---------------------|------------(========)-----------------

                         0            3        5



The problem asks about the intersection of these solution sets (because the service word AND is included to the system).


This intersection is the EMPTY set.  You can see it comparing the plots.


ANSWER.  The solution set of the given system of inequalities is the empty set.