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If x, y, and z are positive with xy = 20, xz = 35, and yz = 14, then what is xyz?

 Apr 24, 2022
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xy = 20    ⇒   y = 20/x

xz = 35   ⇒    z = 35 /x  

yz = 14

 

So

 

yz =   14

 

(20/x) (35/x)  = 14

 

700  =  14 x^2

 

700  / 14   = x^2

 

x^2   = 50

 

x=   5sqrt (2)

 

y = 20  / [ 5sqrt 2]  =   4 / sqrt 2

 

z=  35 / [ 5sqrt 2]  =  7 /sqrt 2

 

So

 

xyz =   5sqrt 2 *   4 /sqrt 2  *   7/ sqrt 2  =     140 / sqrt 2  =  70sqrt 2

 

cool cool cool

 Apr 24, 2022

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