+0

0
18
2

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
0

a) By Cauchy-Schwarz inequality, the maximum is 9/5.

Mar 13, 2023
#2
0

b) z/x = 7/2

Mar 14, 2023