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All-Russian Olympiad
1994 All-Russian Olympiad
1
if (x+\sqrt{x^2 +1}) (y+\sqrt{y^2 +1}) = 1, then x+y = 0.
if (x+\sqrt{x^2 +1}) (y+\sqrt{y^2 +1}) = 1, then x+y = 0.
Source: All Russian MO 1994 ARO IX P1
July 29, 2018
algebra
radical
equation
Problem Statement
Prove that if
(
x
+
x
2
+
1
)
(
y
+
y
2
+
1
)
=
1
(x+\sqrt{x^2 +1}) (y+\sqrt{y^2 +1}) = 1
(
x
+
x
2
+
1
)
(
y
+
y
2
+
1
)
=
1
, then
x
+
y
=
0
x+y = 0
x
+
y
=
0
.
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