Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be the sides of a triangle. No two of them are equal and
λ
∈
R
\lambda \in \mathbb{R}
λ
∈
R
. If the roots of the equation
x
2
+
2
(
a
+
b
+
c
)
x
+
3
λ
(
a
b
+
b
c
+
c
a
)
=
0
x^2 + 2(a + b + c)x + 3\lambda(ab + bc + ca) = 0
x
2
+
2
(
a
+
b
+
c
)
x
+
3
λ
(
ab
+
b
c
+
c
a
)
=
0
are real, then a.
λ
<
4
3
\lambda < \frac{4}{3}
λ
<
3
4
b.
λ
<
5
3
\lambda < \frac{5}{3}
λ
<
3
5
c.
λ
∈
(
1
3
,
5
3
)
\lambda \in \left(\frac{1}{3}, \frac{5}{3}\right)
λ
∈
(
3
1
,
3
5
)
d.
λ
∈
(
4
3
,
5
3
)
\lambda \in \left(\frac{4}{3}, \frac{5}{3}\right)
λ
∈
(
3
4
,
3
5
)
Browse the problem library