Question

Demonstrati ca:
(1-a)(1-b)(1-c)<=8abc
Stiind ca a+b+c=1.

Answer 1

Răspuns:

Explicație pas cu pas:

$(1-a)(1-b)(1-c) =(b+c)(a+c)(a+b)\stackrel{AM-GM}{\geqslant} 2\sqrt{bc}\cdot 2\sqrt{ac}\cdot 2\sqrt{ab}\\=8\sqrt{(abc)^2}=8abc\\\texttt{As simple as that.}$