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2019 Greece Junior Math Olympiad
1
x^2+y^2+25z^2=6xz+8yz and 3x^2+2y^2+z^2=240 (Greece Juniors 2019 p1)
x^2+y^2+25z^2=6xz+8yz and 3x^2+2y^2+z^2=240 (Greece Juniors 2019 p1)
Source:
March 16, 2020
system of equations
algebra
Problem Statement
Find all triplets of real numbers
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
that are solutions to the system of equations
x
2
+
y
2
+
25
z
2
=
6
x
z
+
8
y
z
x^2+y^2+25z^2=6xz+8yz
x
2
+
y
2
+
25
z
2
=
6
x
z
+
8
yz
3
x
2
+
2
y
2
+
z
2
=
240
3x^2+2y^2+z^2=240
3
x
2
+
2
y
2
+
z
2
=
240
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