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JBMO TST - Moldova
2017 Junior Balkan Team Selection Tests - Moldova
Problem 6
Maximum and minimum
Maximum and minimum
Source: Moldova JTST 2017, problem 6
May 3, 2017
algebra
Problem Statement
Let
a
,
b
a,b
a
,
b
and
c
c
c
be real numbers such that
∣
a
+
b
∣
+
∣
b
+
c
∣
+
∣
c
+
a
∣
=
8.
|a+b|+|b+c|+|c+a|=8.
∣
a
+
b
∣
+
∣
b
+
c
∣
+
∣
c
+
a
∣
=
8.
Find the maximum and minimum value of the expression
P
=
a
2
+
b
2
+
c
2
.
P=a^2+b^2+c^2.
P
=
a
2
+
b
2
+
c
2
.
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