Possiblities

Algebra Level 3

If x x , y y and z z are positive real numbers such that x y z = 216 xyz=216 , which one of the options is not a possible value of x y + y z + z x xy+yz+zx ?

433 326 291 96

Aditya Aman by aditya aman , 25, India

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1 solution

Kushal Bose
Feb 8, 2017

Applying A.M.-G.M.

x y + y z + z x ≥ 3 ( x y z ) 2 3 = 3 ( 216 ) 2 / 3 = 3 × 36 = 108 xy+yz+zx \geq 3 (xyz)^{\dfrac{2}{3}}=3 (216)^{2/3}=3 \times 36=108

So, minimum value of x y + y z + z x xy+yz+zx is 108 108 .

So, 96 96 can not be a value

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