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1992 All Soviet Union Mathematical Olympiad
566
ASU 566 Commonwealth of Independent States 1991 x^2/(y-1) + y^2/(x-1)>= 8.
ASU 566 Commonwealth of Independent States 1991 x^2/(y-1) + y^2/(x-1)>= 8.
Source:
August 15, 2019
algebra
inequalities
Problem Statement
Show that for any real numbers
x
,
y
>
1
x, y > 1
x
,
y
>
1
, we have
x
2
y
−
1
+
y
2
x
−
1
≥
8
\frac{x^2}{y - 1}+ \frac{y^2}{x - 1} \ge 8
y
−
1
x
2
+
x
−
1
y
2
≥
8
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