Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
x
\mathbf{x}
x
,
y
\mathbf{y}
y
are two non-zero and non-collinear vectors satisfying
[
(
a
−
2
)
α
2
+
(
b
−
3
)
α
+
c
]
x
+
[
(
a
−
2
)
β
2
+
(
b
−
3
)
β
+
c
]
y
+
[
(
a
−
2
)
γ
2
+
(
b
−
3
)
γ
+
c
]
(
x
×
y
)
=
0
[(a-2)\alpha^2 + (b-3)\alpha + c]\mathbf{x} + [(a-2)\beta^2 + (b-3)\beta + c]\mathbf{y} + [(a-2)\gamma^2 + (b-3)\gamma + c](\mathbf{x} \times \mathbf{y}) = 0
[(
a
−
2
)
α
2
+
(
b
−
3
)
α
+
c
]
x
+
[(
a
−
2
)
β
2
+
(
b
−
3
)
β
+
c
]
y
+
[(
a
−
2
)
γ
2
+
(
b
−
3
)
γ
+
c
]
(
x
×
y
)
=
0
where
α
,
β
,
γ
\alpha, \beta, \gamma
α
,
β
,
γ
are three distinct real numbers, then find the value of
(
a
2
+
b
2
+
c
2
−
4
)
(a^2 + b^2 + c^2 - 4)
(
a
2
+
b
2
+
c
2
−
4
)
.
Browse the problem library