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National and Regional Contests
Netherlands Contests
Dutch IMO TST
2017 Dutch IMO TST
3
algebra problem
algebra problem
Source: Netherlands TST for IMO 2017,day 1 problem 3
February 1, 2018
algebra
Problem Statement
let
x
,
y
x,y
x
,
y
be non-zero reals such that :
x
3
+
y
3
+
3
x
2
y
2
=
x
3
y
3
x^3+y^3+3x^2y^2=x^3y^3
x
3
+
y
3
+
3
x
2
y
2
=
x
3
y
3
find all values of
1
x
+
1
y
\frac{1}{x}+\frac{1}{y}
x
1
+
y
1
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