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8
2009 Algebra #8 - Find Similar Sum
2009 Algebra #8 - Find Similar Sum
Source:
January 2, 2012
AMC
AIME
Problem Statement
If
a
,
b
,
x
a, b, x
a
,
b
,
x
and
y
y
y
are real numbers such that
a
x
+
b
y
=
3
,
ax + by = 3,
a
x
+
b
y
=
3
,
a
x
2
+
b
y
2
=
7
,
ax^2+by^2=7,
a
x
2
+
b
y
2
=
7
,
a
x
3
+
b
x
3
=
16
ax^3+bx^3=16
a
x
3
+
b
x
3
=
16
, and
a
x
4
+
b
y
4
=
42
,
ax^4+by^4=42,
a
x
4
+
b
y
4
=
42
,
find
a
x
5
+
b
y
5
ax^5+by^5
a
x
5
+
b
y
5
.
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