Question

if x²>a² then x>a and x<-a how?

Answer 1

It is not true that x<-a

Answer 2

For example, if x=10 and a=2, then 10² > 2² because 100 > 4, but 10 < -2 is not true.

Answer 3

However, perhaps you meant to say -x < -a?

Answer 4

You can prove that using absolute value...
That's what I learn from our analytic geometry class... :))

Answer 5

Yeah thanx@cebroski but i asked as it was used by friend to solve an answer...

Answer 6

Take the square root of both sides.

Answer 7

sqrt(x^2) = |x|

Answer 8

Hence |x| > |a|
Take cases

Answer 9

If x>0 and a>0 then x>a
If x<0 and a>0 then -x>a
If x<0 and a<0 then x<a

Answer 10

There really is no statement that sums up all three except |x| > |a|

Answer 11

x^2 is positive and (-a)^2 is positive x is less than -a so you a squaring a "bigger negative number" for ex -5 is <-2 (-5)^2 >(-2)^2 5 is bigger than 2

Answer 12

Consider x²>a²
x² - a² > 0
(x-a)(x+a) > 0
So, we know the zeros are a and -a.
Now, draw a graph for x² - a² = 0 (please forgive my poor drawing)

Answer 13

Since x² - a² > 0, we can shade the regions which are bounded by x² - a² = 0 and x-axis with *POSITIVE* y. We get: