If x,y,z are positive real satisfying 4xy+6yz +8zx=9 then greatest value of x y z is - Maths - Sequences and Series

Question

If x,y,z are positive real satisfying 4xy+6yz +8zx=9 then greatest
value of x y z is

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

We know that ,A M ≥ G
M4xy+6yz+8zx3 ≥ 4xy 6yz
8zx1393≥ 192x2y2z213        Since 4xy+6yz+8zx=93≥ 192x2y2z213   Taking cube on both sides , we get27 ≥ 192x2y2z227192 ≥ x2y2z2964≥ x2y2z238 ≥ xyzMaximum value of xyz is 38 
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If x,y,z are positive real satisfying 4xy+6yz +8zx=9 then greatest value of x.y.z is