Hello Can some one please check if i did this question right? Thank you.
-(x-4)^2 (x-1)^2 < 0
so, -(x-4)^2 = 0 and (x-1)^2 =0
so, x=4 and x =1
there fore 1<x<4
Is this correct?
Now if the question is , then the answer will be ALL REAL VALUES ONLY. Can you see the point here?
It's pretty obvious there's a catch because when you first look at it you see a minus sign and you don't think of taking the square root. They're telling you to multiply by -1 to make it positive and then you can take the square root, which is positive by convention, and that gives the quadratic inequality which is the topic of the thread.
As is, it is trivial.
Why do extra work to get the answer? Just simply think about the problem, analyze it, extract the most out of it.
This is a proper way of solving inequality that ensures no lost of solution.
From your solution, when x=-2 the inequality still holds.