MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece JBMO TST
2012 Greece JBMO TST
1
(a-b-c)+(b^2+c^2-bc)=4c^2 (abc-\frac{a^2}{4}-b^2c^2)
(a-b-c)+(b^2+c^2-bc)=4c^2 (abc-\frac{a^2}{4}-b^2c^2)
Source: Greece JBMO TST 2012 p1
April 29, 2019
algebra
equation
system of equations
Problem Statement
Find all triplets of real
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
that solve the equation
a
(
a
−
b
−
c
)
+
(
b
2
+
c
2
−
b
c
)
=
4
c
2
(
a
b
c
−
a
2
4
−
b
2
c
2
)
a(a-b-c)+(b^2+c^2-bc)=4c^2\left(abc-\frac{a^2}{4}-b^2c^2\right)
a
(
a
−
b
−
c
)
+
(
b
2
+
c
2
−
b
c
)
=
4
c
2
(
ab
c
−
4
a
2
−
b
2
c
2
)
Back to Problems
View on AoPS