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Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2017 India PRMO
18
18
Part of
2017 India PRMO
Problems
(1)
2017 preRMO p18, x^2+4y^2+16z^2=48, xy+4yz+2zx=24, x^2 + y^2 + z^2 =?
Source:
8/9/2019
If the real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
are such that
x
2
+
4
y
2
+
16
z
2
=
48
x^2 + 4y^2 + 16z^2 = 48
x
2
+
4
y
2
+
16
z
2
=
48
and
x
y
+
4
y
z
+
2
z
x
=
24
xy + 4yz + 2zx = 24
x
y
+
4
yz
+
2
z
x
=
24
, 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