x^2 + 2x -8 > 0   find x values. x^2 + 2x -8 > 0   find x values.

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x^2 + 2x - 8 > 0

First let us facotor:

x^2 + 2x -8 = (x+4)(x-2) > 0

Then we have two cases:

In order for the function to be positive, then :

(x+4) > 0   AND   (x-2) > 0

==> x > -4    and   x > 2

==> x belongs to (2,inf)...........(1)

The second case is:

(x+4)< 0    AND   (x-2) < 0

==> x < -4     and  x < 2

==> x belongs to (-inf, -4)...........(2)

==> from (1) and (2) we conclude that:

x belongs to (-inf, -4) U (2,inf).

 

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