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If x,y,and z are positive real numbers a...

If x,y,and z are positive real numbers and `x=(12-yz)/(y+z)`. The maximum value of (xyz) equals___________.

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Verified by Experts

The correct Answer is:
8
Consider values xy, yz, zx
Now A.M `ge` G.M
`implies (xy + yz + zx)/(3) ge (x^(2) y^(2) z^(2))^(1//3)`
`implies 4^(3//2) ge xyz`
or `xyz le 8`
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