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Finnish National High School Mathematics Competition
2017 Finnish National High School Mathematics Comp
2
calculate x^2+y^2 and x^4+y^4 when x^3+y^3=2 and x+y=1
calculate x^2+y^2 and x^4+y^4 when x^3+y^3=2 and x+y=1
Source: Finland 2017 p2
September 8, 2019
algebra
system of equations
Problem Statement
Determine
x
2
+
y
2
x^2+y^2
x
2
+
y
2
and
x
4
+
y
4
x^4+y^4
x
4
+
y
4
, when
x
3
+
y
3
=
2
x^3+y^3=2
x
3
+
y
3
=
2
and
x
+
y
=
1
x+y=1
x
+
y
=
1
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