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India Pre-Regional Mathematical Olympiad
2014 India PRMO
5
2014 preRMO p5, a+1=b+2=c+3=d+4=e+5=a+b+c+d+e+3
2014 preRMO p5, a+1=b+2=c+3=d+4=e+5=a+b+c+d+e+3
Source:
August 9, 2019
algebra
Sum of Squares
Problem Statement
If real numbers
a
,
b
,
c
,
d
,
e
a, b, c, d, e
a
,
b
,
c
,
d
,
e
satisfy
a
+
1
=
b
+
2
=
c
+
3
=
d
+
4
=
e
+
5
=
a
+
b
+
c
+
d
+
e
+
3
a + 1 = b + 2 = c + 3 = d + 4 = e + 5 = a + b + c + d + e + 3
a
+
1
=
b
+
2
=
c
+
3
=
d
+
4
=
e
+
5
=
a
+
b
+
c
+
d
+
e
+
3
, what is the value of
a
2
+
b
2
+
c
2
+
d
2
+
e
2
a^2 + b^2 + c^2 + d^2 + e^2
a
2
+
b
2
+
c
2
+
d
2
+
e
2
?
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