MathDB
Problems
Contests
International Contests
Caucasus Mathematical Olympiad
2015 Caucasus Mathematical Olympiad
2
two roots for (x +a) (x+b)=2x+a+b , when a \ne b
two roots for (x +a) (x+b)=2x+a+b , when a \ne b
Source: Caucasus 2015 9.2
April 26, 2019
algebra
roots
trinomial
Problem Statement
Let
a
a
a
and
b
b
b
be arbitrary distinct numbers. Prove that the equation
(
x
+
a
)
(
x
+
b
)
=
2
x
+
a
+
b
(x +a) (x+b)=2x+a+b
(
x
+
a
)
(
x
+
b
)
=
2
x
+
a
+
b
has two different roots.
Back to Problems
View on AoPS