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Question
If x, y, z are positive integers then value of expression (x + y)(y + z)(z + x) is ______.
Options
= 8xyz
> 8xyz
< 8xyz
< 8xyz
Solution
If x, y, z are positive integers then value of expression (x + y)(y + z)(z + x) is > 8xyz.
Explanation:
Since A.M. > G.M.
`(x + y)/2 > sqrt(xy)`
`(y + z)/2 > sqrt(yz)`
And `(z + x)/2 > sqrt(zx)`
Multiplying the three inequalities, we get
`(x + y)/2 * (y + z)/2 * (y + z)/2 > sqrt((xy)(yz)(zx))`
or (x + y)(y + z)(z + x) > 8 xyz
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