We have 4 positive real numbers a, b, c and d such that
a*b = c*d and a - b > c - d.
If (a - b) > (c
- d)
=> (a - b)^2 > (c -
d)^2
=> a^2 - 2ab + b^2 > c^2 - 2cd +
d^2
it is given that ab =
cd
=> a^2 - 2ab + b^2 + 4ab > c^2 - 2cd + d^2
+ 4cd
=> a^2 + 2ab + b^2 > c^2 + 2cd +
d^2
=> (a + b)^2 > (c +
d)^2
=> (a + b) > (c + d) as a, b, c and d
are positive and so are a + b and c + d.
This
proves that given a*b = c*d and a - b > c - d, we have a + b >c +
d.
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