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Purple Comet Problems
2003 Purple Comet Problems
19
Problem 19, Fall 2003 , MS and HS
Problem 19, Fall 2003 , MS and HS
Source:
June 23, 2011
Vieta
Problem Statement
Let
x
1
x_1
x
1
and
x
2
x_2
x
2
be the roots of the equation
x
2
+
3
x
+
1
=
0
x^2 + 3x + 1 = 0
x
2
+
3
x
+
1
=
0
. Compute
(
x
1
x
2
+
1
)
2
+
(
x
2
x
1
+
1
)
2
\left(\frac{x_1}{x_2 + 1}\right)^2 + \left(\frac{x_2}{x_1 + 1}\right)^2
(
x
2
+
1
x
1
)
2
+
(
x
1
+
1
x
2
)
2
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