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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
11.6
log_{x+y} (x^2+y^2)<= 1 (III Soros Olympiad 1996-97 R3 11.6)
log_{x+y} (x^2+y^2)<= 1 (III Soros Olympiad 1996-97 R3 11.6)
Source:
May 31, 2024
logarithms
inequalities
analytic geometry
Problem Statement
On the coordinate plane, draw a set of points
M
(
x
,
y
)
M(x,y)
M
(
x
,
y
)
, the coordinates of which satisfy the inequality
log
x
+
y
(
x
2
+
y
2
)
≤
1.
\log_{x+y} (x^2+y^2) \le 1.
lo
g
x
+
y
(
x
2
+
y
2
)
≤
1.
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