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Soros Olympiad in Mathematics
IV Soros Olympiad 1997 - 98 (Russia)
10.4
2x4 radical system (IV Soros Olympiad 1997-98 Correspondence 10.4)
2x4 radical system (IV Soros Olympiad 1997-98 Correspondence 10.4)
Source:
June 1, 2024
system of equations
algebra
Problem Statement
Solve the system of equations
{
x
+
y
+
z
+
t
=
6
1
−
x
2
+
4
−
y
2
+
9
−
z
2
+
16
−
t
2
=
8
\begin{cases} x+y+z+t=6 \\ \sqrt{1-x^2}+\sqrt{4-y^2}+\sqrt{9-z^2}+\sqrt{16-t^2}=8 \end{cases}
{
x
+
y
+
z
+
t
=
6
1
−
x
2
+
4
−
y
2
+
9
−
z
2
+
16
−
t
2
=
8
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