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I.S.I. B.Math.(Hons.) Admission test : 2010 Problem 4
I.S.I. B.Math.(Hons.) Admission test : 2010 Problem 4
Source:
April 10, 2012
inequalities
inequalities proposed
Problem Statement
If
a
,
b
,
c
∈
(
0
,
1
)
a,b,c\in (0,1)
a
,
b
,
c
∈
(
0
,
1
)
satisfy
a
+
b
+
c
=
2
a+b+c=2
a
+
b
+
c
=
2
, prove that
a
b
c
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
≥
8
\frac{abc}{(1-a)(1-b)(1-c)}\ge 8
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
ab
c
≥
8
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