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Malaysia National Olympiad
2019 Malaysia National Olympiad
B1
B1
Part of
2019 Malaysia National Olympiad
Problems
(1)
Problem B1
Source: 2019 Malaysia OMK
8/21/2019
Given three nonzero real numbers
a
,
b
,
c
,
a,b,c,
a
,
b
,
c
,
such that
a
>
b
>
c
a>b>c
a
>
b
>
c
, prove the equation has at least one real root.
1
x
+
a
+
1
x
+
b
+
1
x
+
c
−
3
x
=
0
\frac{1}{x+a}+\frac{1}{x+b}+\frac{1}{x+c}-\frac{3}{x}=0
x
+
a
1
+
x
+
b
1
+
x
+
c
1
−
x
3
=
0
@below sorry, I believe I fixed it with the added constraint.
algebra