Question

cho 0<a,b,c,d<1.chứng minh rằng (1-a)(1-b)(1-c)(1-d)>1-a-b-c-d

Answer 1

\(\left(1-a\right)\left(1-b\right)\left(1-c\right)\left(1-d\right)\)

\(=abcd+bd+cd+ab\left(1-c\right)+ad\left(1-b\right)+ac\left(1-d\right)+bc\left(1-d\right)+\left(1-a-b-c-d\right)\)

\(>1-a-b-c-d\)