SOLUTION: If {{{ a > 0 }}} show that the solution set of the inequality {{{ x^2 > a }}} consists of all numbers x for which {{{ x < - sqrt(a) }}} or {{{ x > sqrt(a) }}}. I figured it out

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Question 660769: If show that the solution set of the inequality consists of all numbers x for which or .
I figured it out all the way to the point from here ,when I try to solve for x by setting each factor as greater than 0, I get the opposite result of what I need, i.e. instead of and I don't know why. Thanks so much again!
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

Just looking at the signs of the 2 factors,
Neither factor can be
These 2 cases work:
(+) * (+) >0
( - ) * ( - ) > 0
------------
These don't work:
(+) * (-)
( - ) * (+)
--------
The 1st case:
(+) * (+) >0


and


----------------
Both of these have to be true. They are only
true if the 1st is true, so
must hold
---------------
The 2nd case
(-)*(-) >0


and


-------------
Both of these have to be true. They are only true
if
----------------
so, or
since either of the 2 cases works


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