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JBMO TST - Turkey
2018 JBMO TST-Turkey
1
1
Part of
2018 JBMO TST-Turkey
Problems
(1)
3 eqaul numbers and prove that x=1
Source: 2018 JBMO TST - Turkey, P1
3/27/2020
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be distinct real numbers and
x
x
x
be a real number. Given that three numbers among
a
x
2
+
b
x
+
c
,
a
x
2
+
c
x
+
b
,
b
x
2
+
c
x
+
a
,
b
x
2
+
a
x
+
c
,
c
x
2
+
a
x
+
b
,
c
x
2
+
b
x
+
a
ax^2+bx+c, ax^2+cx+b, bx^2+cx+a, bx^2+ax+c, cx^2+ax+b, cx^2+bx+a
a
x
2
+
b
x
+
c
,
a
x
2
+
c
x
+
b
,
b
x
2
+
c
x
+
a
,
b
x
2
+
a
x
+
c
,
c
x
2
+
a
x
+
b
,
c
x
2
+
b
x
+
a
coincide, prove that
x
=
1
x=1
x
=
1
.
algebra