Maximize the value

Algebra Level 3

If the sum of three positive numbers is 1 and the maximum value of their product is a a , find the value of 1 a \frac{1}{a} .


The answer is 27.

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Swapnil Roge by Swapnil Roge , 23, India

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1 solution

Rishabh Jain
Dec 30, 2015

Let the numbers be x,y,z

x+y+z=1> 3 ( x y z ) 1 / 3 ⇒ 3(xyz)^{1/3}\Rightarrow xyz≤1/27=1/a

⇒ \Rightarrow a=27

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah, simple application of AM GM.

Swapnil Das - 5 years, 5 months ago

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