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12
x^3+a^3x^2+b^3x+c^3=0
x^3+a^3x^2+b^3x+c^3=0
Source:
October 28, 2010
algebra unsolved
algebra
Problem Statement
The equation
x
3
+
a
x
2
+
b
x
+
c
=
0
x^3 + ax^2 + bx + c = 0
x
3
+
a
x
2
+
b
x
+
c
=
0
has three (not necessarily distinct) real roots
t
,
u
,
v
t, u, v
t
,
u
,
v
. For which
a
,
b
,
c
a, b, c
a
,
b
,
c
do the numbers
t
3
,
u
3
,
v
3
t^3, u^3, v^3
t
3
,
u
3
,
v
3
satisfy the equation
x
3
+
a
3
x
2
+
b
3
x
+
c
3
=
0
x^3 + a^3x^2 + b^3x + c^3 = 0
x
3
+
a
3
x
2
+
b
3
x
+
c
3
=
0
?
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