Inequalities

**Petrus** · January 10th 2013, 05:56 AM

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)

**emakarov** · January 10th 2013, 06:50 AM

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."

**Petrus** · January 10th 2013, 07:29 AM

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

**HallsofIvy** · January 10th 2013, 08:10 AM

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.