MathDB
Problems
Contests
National and Regional Contests
India Contests
ISI Entrance Examination
2015 ISI Entrance Examination
5
5
Part of
2015 ISI Entrance Examination
Problems
(1)
Show it has *exactly* n roots
Source: ISI Entrance 2015
5/10/2015
If
0
<
a
1
<
⋯
<
a
n
0<a_1< \cdots < a_n
0
<
a
1
<
⋯
<
a
n
, show that the following equation has exactly
n
n
n
roots.
a
1
a
1
−
x
+
a
2
a
2
−
x
+
a
3
a
3
−
x
+
⋯
+
a
n
a
n
−
x
=
2015
\frac{a_1}{a_1-x}+\frac{a_2}{a_2-x}+ \frac{a_3}{a_3-x}+ \cdots + \frac {a_n}{a_n - x} = 2015
a
1
−
x
a
1
+
a
2
−
x
a
2
+
a
3
−
x
a
3
+
⋯
+
a
n
−
x
a
n
=
2015
algebra
isi