Use algebraic manipulation to find the minimum sum of products expression for th

Question

Use algebraic manipulation to find the minimum sum of products expression for the following expression for function:
f=x1x2'x3' + x1x2x4 + x1x2'x2x4'

I'm lost on this, any explanation would be greatly appreciated. It is problem 2.13 in the textbook Fundamentals of Digital Logic with Verilog Design 2nd Edition by Stephen Brown and Zvonko Vranesic. Thanks.

Explanation / Answer

We know that AM >= GM or, (x1x2'x3' + x1x2x4 + x1x2'x2x4')/3 >=[(x1x2'x3')*(x1x2x4)*( x1x2'x2x4')]^(1/3) So ,(x1x2'x3' + x1x2x4 + x1x2'x2x4')/3 >=[x1^3*x2'^2*x3'*x3*x4*x4']^(1/3) So minimum value =3*[x1^3*x2'^2*x3'*x3*x4*x4']^(1/3)

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