Set of OSK 2016

Calculus Level 3

Given real numbers a a and b b such that a − b = 20 \sqrt a - \sqrt b = 20 . Find the maximum value of a − 5 b a - 5b .

Source : OSK 2016.


The answer is 500.

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Arya Kusuma by Arya Kusuma , 22, Indonesia

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1 solution

Arya Kusuma
Sep 27, 2016

a \sqrt{a} - b \sqrt{b} = 20 ⇒ \Rightarrow a = b + 40 b \sqrt{b} + 400

a - 5b = b + 40 b \sqrt{b} + 400 - 5b = -4 ( b (\sqrt{b} - 5)^2 + 500

Hence, the maximum value of a - 5b is 500, reach when a = 625 and b = 25

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