lean_workbook_plus_4582

Let $a,\ b,\ c,\ d$ be real numbers such that $(a-1)(b-1)(c-1)(d-1)=1$ . For $a\geq 2,\ b\geq 2,\ c\geq 2,\ d\geq 2$ , prove that $\ \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}\geq 2$ .