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Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2013 India PRMO
11
11
Part of
2013 India PRMO
Problems
(1)
2013 preRMO p11 x^2+6y=-17, y^2+4z=1, z^2+2x=2, x^2 + y^2 + z^2 ?
Source:
8/8/2019
Three real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
are such that
x
2
+
6
y
=
ā
17
,
y
2
+
4
z
=
1
x^2 + 6y = -17, y^2 + 4z = 1
x
2
+
6
y
=
ā
17
,
y
2
+
4
z
=
1
and
z
2
+
2
x
=
2
z^2 + 2x = 2
z
2
+
2
x
=
2
. What is the value of
x
2
+
y
2
+
z
2
x^2 + y^2 + z^2
x
2
+
y
2
+
z
2
?
algebra
system of equations