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Part a)

 

For positive real numbers x, y, z and  what is the maximum possible value for

 

\( \sqrt{\frac{3x+4y}{6x+5y+4z}} + \sqrt{\frac{y+2z}{6x+5y+4z}} + \sqrt{\frac{2z+3x}{6x+5y+4z}}? \)
 

 

Part b)

 

Find \(\frac {z} {x}\) if \((x, y, z)\) is a triple that gives the maximum value in Part a.

 Mar 13, 2023
 #1
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a) By Cauchy-Schwarz inequality, the maximum is 9/5.

 Mar 13, 2023
 #2
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b) z/x = 7/2

 Mar 14, 2023

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