+773 Check out this: https://web2.0calc.com/questions/please-help_29548#r1
Similar, but not really, might help you with a boost...................!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
^m^, whymenotsmart
+23246 Solve the inequality: (x - 1)(x + 1) > 2
Multiply out: x2 - 1 > 2
Get one side to be zero: x2 - 3 > 0
Factor: [ x + sqrt(3) ] · [ x - sqrt(3) ] > 0
The number line is now broken into 5 regions:
x < - sqrt(3) x = - sqrt(3) - sqrt(x) < x < sqrt(3) sqrt(3) x > sqrt(3)
Test each of these regions, one at a time:
-- for x < - sqrt(3) choose a number smaller than - sqrt(3)
I'm going to choose -10.
Does -10 work in the inequality x2 - 3 > 0 --> (-10)2 - 3 > 0 ---> 100 - 3 > 0
Yes, that's true! So the region x < - sqrt(3) is part of the answer.
-- for x = - sqrt(3) This doesn't work because there is no equal sign in the original problem.
-- for - sqrt(x) < x < sqrt(3) choose a number in this region
I'm going to choose 0.
Does 0 work in the inequality x2 - 3 > 0 --> (0)2 - 3 > 0 ---> 0 - 3 > 0
No, that's not true ... so this region is not part of the answer.
-- for x = sqrt(3) This doesn't work because there is no equal sign in the original problem.
-- for x > sqrt(3) choose a number greater than sqrt(3)
I'm going to choose 10.
Does 10 work in the inequality x2 - 3 > 0 --> (10)2 - 3 > 0 ---> 100 - 3 > 0
Yes, that's true! So the region x > sqrt(3) is also part of the answer.
So, the answer is: either x < - sqrt(3) or x > sqrt(3)
