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EGMO TST - Moldova
2021 Moldova EGMO TST
12
\frac{\sqrt{x^2+4}}{\sqrt{x^2+1}+\sqrt{x^2+9}}
\frac{\sqrt{x^2+4}}{\sqrt{x^2+1}+\sqrt{x^2+9}}
Source: Moldova EGMO TST 2021
February 4, 2023
algebra
Problem Statement
Find all real numbers
y
y
y
, for which there exists at least one real number
x
x
x
such that
y
=
x
2
+
4
x
2
+
1
+
x
2
+
9
.
y=\frac{\sqrt{x^2+4}}{\sqrt{x^2+1}+\sqrt{x^2+9}}.
y
=
x
2
+
1
+
x
2
+
9
x
2
+
4
.
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