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1
Romania District Olympiad 2008 - Grade XI
Romania District Olympiad 2008 - Grade XI
Source:
April 10, 2011
linear algebra
linear algebra unsolved
Problem Statement
If
A
∈
M
2
(
R
)
A\in \mathcal{M}_2(\mathbb{R})
A
∈
M
2
(
R
)
, prove that:
det
(
A
2
+
A
+
I
2
)
≥
3
4
(
1
−
det
A
)
2
\det(A^2+A+I_2)\ge \frac{3}{4}(1-\det A)^2
det
(
A
2
+
A
+
I
2
)
≥
4
3
(
1
−
det
A
)
2
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