MathDB
Problems
Contests
National and Regional Contests
Germany Contests
QEDMO
2007 QEDMO 5th
3
a=b+c+d-2\sqrt{bc+cd+db} if d=a+b+c+2\sqrt{ab+bc+ca}
a=b+c+d-2\sqrt{bc+cd+db} if d=a+b+c+2\sqrt{ab+bc+ca}
Source: 5th QEDMO 2007 p3
November 9, 2020
algebra
Problem Statement
Let
a
,
a,
a
,
b
,
b,
b
,
c
,
c,
c
,
d
d
d
be four positive reals such that
d
=
a
+
b
+
c
+
2
a
b
+
b
c
+
c
a
.
d=a+b+c+2\sqrt{ab+bc+ca}.
d
=
a
+
b
+
c
+
2
ab
+
b
c
+
c
a
.
Prove that
a
=
b
+
c
+
d
−
2
b
c
+
c
d
+
d
b
.
a=b+c+d-2\sqrt{bc+cd+db}.
a
=
b
+
c
+
d
−
2
b
c
+
c
d
+
d
b
.
Darij Grinberg
Back to Problems
View on AoPS