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1969 All Soviet Union Mathematical Olympiad
118
ASU 118 All Soviet Union MO 1969 a+b<c+d, (a+b)(c+d)<ab+cd, (a+b)cd<ab(c+d)
ASU 118 All Soviet Union MO 1969 a+b<c+d, (a+b)(c+d)<ab+cd, (a+b)cd<ab(c+d)
Source:
June 23, 2019
inequalities
algebra
Problem Statement
Given positive numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
. Prove that the set of inequalities
a
+
b
<
c
+
d
a+b<c+d
a
+
b
<
c
+
d
(
a
+
b
)
(
c
+
d
)
<
a
b
+
c
d
(a+b)(c+d)<ab+cd
(
a
+
b
)
(
c
+
d
)
<
ab
+
c
d
(
a
+
b
)
c
d
<
a
b
(
c
+
d
)
(a+b)cd<ab(c+d)
(
a
+
b
)
c
d
<
ab
(
c
+
d
)
contain at least one wrong.
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