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1000
Shifted Power Sums
Editorial
algebra
symmetric expressions
power sums
polynomials
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be real numbers satisfying
a
+
b
+
c
=
3
,
a
2
+
b
2
+
c
2
=
7
,
a
3
+
b
3
+
c
3
=
15.
a + b + c = 3, \qquad a^2 + b^2 + c^2 = 7, \qquad a^3 + b^3 + c^3 = 15.
a
+
b
+
c
=
3
,
a
2
+
b
2
+
c
2
=
7
,
a
3
+
b
3
+
c
3
=
15.
Find
(
a
−
1
)
3
+
(
b
−
1
)
3
+
(
c
−
1
)
3
(a-1)^3 + (b-1)^3 + (c-1)^3
(
a
−
1
)
3
+
(
b
−
1
)
3
+
(
c
−
1
)
3
.
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