mossy oak
I'm trying to prepare for an olympiad, and in one of given tasks (with an inequality) the solution comes down to the inequality at the top. I tried to solve it using the method of intervals, as usual, but It didn't help, and the actual answer is xє[1;2]. The solution to the problem doesn't explain how to solve this thing, and I couldn't find anything similar on the web. What is a method for solving these?
deep streamBOT
rustic ether
can barely see anything
open finch
I don't think that you had the correct problem. Look to all terms in the left side of inequality, you have only positive terms. Thus, the answer will be all real values minus 0, because the denominator...
Look for the graph of the left side
All the values of left side is above or equal 0
mossy oak
Sorry for the delay, and I double checked the answer, it's indeed different, but it doesn't matter here. The main point is how do I solve such inequalities at all
open finch
Ah, ok. That type of inequality can be solved by several types. What do you must take in mind is, as the left side must be greater or equal zero, this fact lead us to make the fraction greater or equal zero. So you can start by taking the fraction equals zero. This way, only numerator have to be zero. So you do that. In this specific case, split this two terms and equal to zero each one of them. After that, you must proceed to make the fraction greater than zero. Maybe this is the must troubled part, because you need to make the correct analysis as much is needed. So, remember that, for fractions, these are positive when the numerator and denominator are positive or are negative. So, for each case you need to make the sign analysis to guarantee that will occur...
Maybe, this video can help you
mossy oak
Oh, I see now. My mistake was that I used a "quick interval method" which my tutor taught me a few months ago. It works with simple inequalities where no functions occur. But when we have functions in sight, we must make a deeper analysis
Now I see I already have enough knowledge for solving this thing, thanks