Problem Solving

What is the minimum value of (ab+ac+ad+bc+bd+cd)? If abcd = 16.

A.51
B.26
C.12
D.24
E.49
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Hit & Trial Method...

simply take a=b=c=d => This gives a=b=c=d = 2 each.

Now put a=b=c=d = 2 in (ab+ac+ad+bc+bd+cd);

we get (ab+ac+ad+bc+bd+cd) as 24.

You may try with other combinations for a, b, c, d as say 1, 1, 1, 16 or something other.

In each case you will land up greater value than 24.

Algebraic approach...

To get sum of few variables to be minimum, their product should be constant & all should be equal to each other.

pl. see this https://www.beatthegmat.com/must-see-for ... 09814.html

so for (ab+ac+ad+bc+bd+cd) to be min. => ab.ac.ad.bc.bd.cd should be constant.

ab.ac.ad.bc.bd.cd = (abcd)^3 = 16^3 (constant)