Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
α
,
β
\alpha, \beta
α
,
β
and
γ
\gamma
γ
are the cube roots of
p
p
p
(
p
<
0
p < 0
p
<
0
), then for any
x
,
y
x, y
x
,
y
and
z
z
z
,
x
α
+
y
β
+
z
γ
x
β
+
y
γ
+
z
α
\frac{x\alpha + y\beta + z\gamma}{x\beta + y\gamma + z\alpha}
x
β
+
y
γ
+
z
α
xα
+
y
β
+
z
γ
is equal to a.
1
2
(
−
1
−
i
3
)
,
i
=
−
1
\frac{1}{2}(-1 - i\sqrt{3}), i = \sqrt{-1}
2
1
(
−
1
−
i
3
)
,
i
=
−
1
b.
1
2
(
1
+
i
3
)
,
i
=
−
1
\frac{1}{2}(1 + i\sqrt{3}), i = \sqrt{-1}
2
1
(
1
+
i
3
)
,
i
=
−
1
c.
1
2
(
1
−
i
3
)
,
i
=
−
1
\frac{1}{2}(1 - i\sqrt{3}), i = \sqrt{-1}
2
1
(
1
−
i
3
)
,
i
=
−
1
d. None of these
Browse the problem library