Answer to Question #15640 in Abstract Algebra for Aziza
G = √(ab).
We know that
2a + 5b = 10 ==> a = 5 - 2.5b,
G = √(ab) = √((5 - 2.5b)b) = √(5b - 2.5b²).
G reachs its maximum value when 5b - 2.5b² do, so let's maximise it with respect to b:
(5b - 2.5b²)' = 5 - 5b;
5 - 5b = 0 <==> b = 1.
Therefore, b=1 maximises G.
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