Are there restrictions on the range of values for a and b? For example, can one be negative and the other positive?
Assuming that they are always the same sign, then for
((a+b)^2)/(4*a*b) to be greater than one, it would need to be true that:
(a+b)^2 > 4*a*b
Now here's where my question about restrictions on the values of a and b comes in. (a+b)^2 is always positive, so if 4ab is negative (ie, if a and b have different signs), then
(a+b)^2 > 4*a*b
is true (a positive value is always greater than a negative).
However, if 4ab is negative, then
((a+b)^2)/(4*a*b)
is also negative, in which case it could not be greater than one.
Are there any restrictions on the values of a and b?
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PS
Take Two:
If ((a+b)^2)/(4*a*b) > 1, then (a+b)^2 > 4*a*b
a^2 + 2ab + b^2 > 4ab
a^2 - 2ab +b^2 > 0
(a-b)^2 > 0
a - b > 0
a > b
So we also have a requirement that a be greater than b?
Edited by dwise1, : add attempt at proof