1. ## 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)

2. ## 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."

3. ## Re: Inequalities

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

4. ## Re: Inequalities

If $\displaystyle x^2- 77> 0$ then $\displaystyle x^2> 77$ so, taking the square root of both sides, either $\displaystyle x> \sqrt{77}$ or $\displaystyle x< -\sqrt{77}$ which is the same as $\displaystyle |x|> \sqrt{77}$. Now, $\displaystyle \sqrt{77}= 8.77$ so that $\displaystyle |x|> 8.77$. Of course, if $\displaystyle |x|> 8.77$ 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.

5. ## 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

6. ## Re: Inequalities

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.
$\displaystyle x=-9$ is a solution for $\displaystyle x^2-77>0$. BUT $\displaystyle -9\not>5$.