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Question

If x, y, z are distinct positive integers then value of expression (x + y) (y + z) (z + x) is

A
is equal to 8xyz
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B
is greater than 8xyz
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C
is smaller than 8xyz
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D
is equal to 4xyz
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Solution

The correct option is B is greater than 8xyz

Since x, y, z are distinct positive integers.A.M. > G.M. (Equality doesn't hold because the numbers are distinct)⇒x+y2>√xy, y+z2>√yz, z+x2>√zxMultiplying the three inequalities, we get,⇒(x+y2)(y+z2)(z+x2)>√xy×yz×zxNote: When both the sides of inequalities are positive and we multiply the inequalities, then the inequality sign remain the same.In general, if we don't know the signs of both the sides of inequalities, then we can't multuply them.⇒(x+y)(y+z)(z+x)>8xyz

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