Answer:
-48/7 < a/2b-2b/a < -11/30
Explanation:
a/2b - 2b/a
Get a common denominator of 2ab
a/2b * a/a - 2b/a *2b/2b
a^2/2ab - 4b^2/2ab
(a^2-4b^2)/2ab
We want to find out the minimum and maximum for the expression
Minimum:
a needs to be the smallest and b needs to be the largest
2^2 -4* 7^2 4-196 -192 -48
------------- = ---------- = ----------= ---------
2*2*7 28 28 7
The maximum is when a is the largest and b is the smallest
5^2 - 4*3^2 25-36 -11
----------------- = ---------- = ---------- =
2*5*3 30 30
The expression is between
-48/7 < a/2b-2b/a < -11/30