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Spain Mathematical Olympiad
1971 Spain Mathematical Olympiad
3
(px + qy)^2 <= px^2 + qy^2 if 0 < p, 0 < q, p +q < 1
(px + qy)^2 <= px^2 + qy^2 if 0 < p, 0 < q, p +q < 1
Source: Spanish Mathematical Olympiad 1971 P3
December 5, 2022
algebra
inequalities
Problem Statement
If
0
<
p
0 < p
0
<
p
,
0
<
q
0 < q
0
<
q
and
p
+
q
<
1
p +q < 1
p
+
q
<
1
prove
(
p
x
+
q
y
)
2
≤
p
x
2
+
q
y
2
(px + qy)^2 \le px^2 + qy^2
(
p
x
+
q
y
)
2
≤
p
x
2
+
q
y
2
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