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International Contests
Czech-Polish-Slovak Match
1995 Czech and Slovak Match
4
4
Part of
1995 Czech and Slovak Match
Problems
(1)
minimum (x+y) when (x+\sqrt{1+x^2})(y+\sqrt{1+y^2}) = p
Source: Czech and Slovak Match 1995 P4
10/1/2017
For each real number
p
>
1
p > 1
p
>
1
, find the minimum possible value of the sum
x
+
y
x+y
x
+
y
, where the numbers
x
x
x
and
y
y
y
satisfy the equation
(
x
+
1
+
x
2
)
(
y
+
1
+
y
2
)
=
p
(x+\sqrt{1+x^2})(y+\sqrt{1+y^2}) = p
(
x
+
1
+
x
2
)
(
y
+
1
+
y
2
)
=
p
.
minimum value
algebra
Sum