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National and Regional Contests
Bulgaria Contests
Bulgaria JBMO Team Selection Test
2016 Bulgaria JBMO TST
1
Algebra proposed
Algebra proposed
Source: Bulgaria 2016 JTST P1 day 2
August 27, 2019
algebra proposed
algebra
Problem Statement
a
,
b
,
c
,
d
,
e
,
f
a,b,c,d,e,f
a
,
b
,
c
,
d
,
e
,
f
are real numbers. It is true that:
a
+
b
+
c
+
d
+
e
+
f
=
20
a+b+c+d+e+f=20
a
+
b
+
c
+
d
+
e
+
f
=
20
(
a
−
2
)
2
+
(
b
−
2
)
2
+
.
.
.
+
(
f
−
2
)
2
=
24
(a-2)^2+(b-2)^2+...+(f-2)^2=24
(
a
−
2
)
2
+
(
b
−
2
)
2
+
...
+
(
f
−
2
)
2
=
24
Find the maximum value of d.
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