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1981 All Soviet Union Mathematical Olympiad
319
ASU 319 All Soviet Union MO 1981 0<=x,y and x^3+y^3=x-y => x^2+y^2<1.
ASU 319 All Soviet Union MO 1981 0<=x,y and x^3+y^3=x-y => x^2+y^2<1.
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July 23, 2019
algebra
inequalities
Problem Statement
Positive numbers
x
,
y
x,y
x
,
y
satisfy equality
x
3
+
y
3
=
x
ā
y
x^3+y^3=x-y
x
3
+
y
3
=
x
ā
y
Prove that
x
2
+
y
2
<
1
x^2+y^2<1
x
2
+
y
2
<
1
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