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Algebra Level 4

Calculate the minimum value of the following expression if $\{a_1, a_2, a_3, a_4, a_5, a_6\} = \{1; 2; 3; 4; 5; 6\}$ .

$\large (a_1 + a_2 + a_3)(a_3 + a_4 + a_5)(a_5 + a_6 + a_1)$

1 solution

X X
Feb 8, 2019

The sum of the three brackets is $2(a_1+a_3+a_5)+a_2+a_4+a_6$

Let the sum be the smallest. So let $a_1=1,a_3=2,a_5=3$

The product becomes $(3+a_2)(5+a_4)(4+a_6)$

The sum of the brackets is constant( $=27$ )

Let gaps of the values of each bracket be bigger, so the output would be smaller.

Hence let $a_2=4,a_4=6,a_6=5$ . The product becomes 693.