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India Pre-Regional Mathematical Olympiad
2012 India PRMO
17
2012 preRMO p17, roots of equation x^3 + 3x + 5 = 0
2012 preRMO p17, roots of equation x^3 + 3x + 5 = 0
Source:
June 17, 2019
Problem Statement
Let
x
1
,
x
2
,
x
3
x_1,x_2,x_3
x
1
,
x
2
,
x
3
be the roots of the equation
x
3
+
3
x
+
5
=
0
x^3 + 3x + 5 = 0
x
3
+
3
x
+
5
=
0
. What is the value of the expression
(
x
1
+
1
x
1
)
(
x
2
+
1
x
2
)
(
x
3
+
1
x
3
)
\left( x_1+\frac{1}{x_1} \right)\left( x_2+\frac{1}{x_2} \right)\left( x_3+\frac{1}{x_3} \right)
(
x
1
+
x
1
1
)
(
x
2
+
x
2
1
)
(
x
3
+
x
3
1
)
?
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