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2000 Switzerland Team Selection Test
6
6
Part of
2000 Switzerland Team Selection Test
Problems
(1)
\sqrt{7x+3}+ \sqrt{7y+3}+\sqrt{7z+3} \le 7 when x,y,z have sum 1
Source: Switzerland - Swiss TST 2000 p6
2/19/2020
Positive real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
have the sum
1
1
1
. Prove that
7
x
+
3
+
7
y
+
3
+
7
z
+
3
≤
7
\sqrt{7x+3}+ \sqrt{7y+3}+\sqrt{7z+3} \le 7
7
x
+
3
+
7
y
+
3
+
7
z
+
3
≤
7
. Can number
7
7
7
on the right hand side be replaced with a smaller constant?
inequalities
Sum
algebra