1+x^2÷2x^2-21x+40<0 please give me answer with explanation
Answer (1)
19th May, 2020
Hi
Since the numerator is 1+x^2, it is always >0.
For the inequality to hold, the LHS should be less than 0 or negative.
This means that the denominator of LHS should be negative now.
=> 2x^2-21x+40<0
Doing middle term split,
2x^2-5x-16x+40= x(2x-5)-8(2x-5)<0
We get two boundaries for x, x=8 and x=2/5
Clearly you can see that the expression will be negative between these 2 values of x,i.e x should lie in (2/5,8)
Hope this helps!
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