# Inequalities

• January 10th 2013, 05:56 AM
Petrus
Inequalities
which one (s) of the following inequalities are then known to be x^2-77> 0
a) x>-5
b)x>5
c)lxl>5

this is an old exam i train and the answer shall be c) but idk how they do it.. My progress is that i solve x>sqrt(77)
• January 10th 2013, 06:50 AM
emakarov
Re: Inequalities
I don't understand the question (probably a language issue). If X is known to be Y, then X is Y and this fact is known. None of the inequalities from the answers literally are x^2 - 77 > 0. Try rephrasing your question using the word "implies."
• January 10th 2013, 07:29 AM
Petrus
Re: Inequalities
Quote:

Originally Posted by emakarov
I don't understand the question (probably a language issue). If X is known to be Y, then X is Y and this fact is known. None of the inequalities from the answers literally are x^2 - 77 > 0. Try rephrasing your question using the word "implies."

I Will do it soon:) i used google translate:P
• January 10th 2013, 08:10 AM
HallsofIvy
Re: Inequalities
If $x^2- 77> 0$ then $x^2> 77$ so, taking the square root of both sides, either $x> \sqrt{77}$ or $x< -\sqrt{77}$ which is the same as $|x|> \sqrt{77}$. Now, $\sqrt{77}= 8.77$ so that $|x|> 8.77$. Of course, if $|x|> 8.77$ then it is certainly true that |x|> 5. Although that is not the "best" inequality, it is the only one of the given answers that is true.
• January 10th 2013, 08:39 AM
Petrus
Re: Inequalities
Should not b also be true x>5? Idk i kinda think it was a bad question they had on a old exam
• January 10th 2013, 09:00 AM
Plato
Re: Inequalities
Quote:

Originally Posted by Petrus
Should not b also be true x>5? Idk i kinda think it was a bad question they had on a old exam

No.
$x=-9$ is a solution for $x^2-77>0$. BUT $-9\not>5$.