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2020 China Northern MO
BP2
Non-symmetric Inequality to Prove
Non-symmetric Inequality to Prove
Source: 2020 China North Mathematical Olympiad Basic Level P2
August 4, 2020
inequalities
algebra
Problem Statement
Given
a
,
b
,
c
∈
R
a,b,c \in \mathbb{R}
a
,
b
,
c
∈
R
satisfying
a
+
b
+
c
=
a
2
+
b
2
+
c
2
=
1
a+b+c=a^2+b^2+c^2=1
a
+
b
+
c
=
a
2
+
b
2
+
c
2
=
1
, show that
−
1
4
≤
a
b
≤
4
9
\frac{-1}{4} \leq ab \leq \frac{4}{9}
4
−
1
≤
ab
≤
9
4
.
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