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Saint Petersburg Mathematical Olympiad
2018 Saint Petersburg Mathematical Olympiad
4
Equation without roots
Equation without roots
Source: St Petersburg Olympiad 2018, Grade 11, P4
June 21, 2018
algebra
inequalities
Problem Statement
(
b
+
c
)
x
2
+
(
a
+
c
)
x
+
(
a
+
b
)
=
0
(b+c)x^2+(a+c)x+(a+b)=0
(
b
+
c
)
x
2
+
(
a
+
c
)
x
+
(
a
+
b
)
=
0
has not real roots. Prove that
4
a
c
−
b
2
≤
3
a
(
a
+
b
+
c
)
4ac-b^2 \leq 3a(a+b+c)
4
a
c
−
b
2
≤
3
a
(
a
+
b
+
c
)
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