Xavier Aptitude Test 2013 Paper

Question : 61 of 121

Marks: +1, -0

Consider the expression

\ {\ (a^{2}+a+l )\ (b^{2}+b+1\ ) (c^{2}+c+l\ )\ (d^{2}+d+1\ \ (e^{2}+e+1\ )}/{a b c d e}

Where a, b, c, d and e are positive numbers. The minimum value of the expression is

Solution:

(e)

\ {a^{2}+a+1}/{3} \≥(a^{2} \× a × 1 )^{1 / 3} \ .....

ByAM - GM relation
Hence,

\ {a^{2}+a+1}/{3} \≥

a or

\ {a^{2}+a+1}/{a} ≥ 3

Similarly, a similar relation for b, c, d and e and then multiplying, we get

\ {\ (a^{2}+a+1 )\ (b^{2}+b+1 )\ (c^{2}+c+1\ )\ (d^{2}+d+1\ ) (e^{2}+e+1\ )}/{a b c d e}

\≥ 3^{5}=243

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