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Swedish Mathematical Competition
1991 Swedish Mathematical Competition
2
2
Part of
1991 Swedish Mathematical Competition
Problems
(1)
y - \sqrt{y} < x - 1/4 < y + \sqrt{y} if x - \sqrt{x} < y - 1/4 <= x + \sqrt{x}
Source: 1991 Swedish Mathematical Competition p2
4/2/2021
x
,
y
x, y
x
,
y
are positive reals such that
x
−
x
≤
y
−
1
/
4
≤
x
+
x
x - \sqrt{x} \le y - 1/4 \le x + \sqrt{x}
x
−
x
≤
y
−
1/4
≤
x
+
x
. Show that
y
−
y
≤
x
−
1
/
4
≤
y
+
y
y - \sqrt{y} \le x - 1/4 \le y + \sqrt{y}
y
−
y
≤
x
−
1/4
≤
y
+
y
.
inequalities
algebra