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88
Find the range of w(w + x)(w + y)(w + z)
Find the range of w(w + x)(w + y)(w + z)
Source:
September 14, 2010
algebra
polynomial
calculus
binomial theorem
algebra unsolved
Problem Statement
Determine the range of
w
(
w
+
x
)
(
w
+
y
)
(
w
+
z
)
w(w + x)(w + y)(w + z)
w
(
w
+
x
)
(
w
+
y
)
(
w
+
z
)
, where
x
,
y
,
z
x, y, z
x
,
y
,
z
, and
w
w
w
are real numbers such that
x
+
y
+
z
+
w
=
x
7
+
y
7
+
z
7
+
w
7
=
0.
x + y + z + w = x^7 + y^7 + z^7 + w^7 = 0.
x
+
y
+
z
+
w
=
x
7
+
y
7
+
z
7
+
w
7
=
0.
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