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3
HMMT Algebra/NT 2019/3: Twist on standard t^3 + 1/t^3 problem
HMMT Algebra/NT 2019/3: Twist on standard t^3 + 1/t^3 problem
Source:
February 17, 2019
HMMT
algebra
Problem Statement
Let
x
x
x
and
y
y
y
be positive real numbers. Define
a
=
1
+
x
y
a = 1 + \tfrac{x}{y}
a
=
1
+
y
x
and
b
=
1
+
y
x
b = 1 + \tfrac{y}{x}
b
=
1
+
x
y
. If
a
2
+
b
2
=
15
a^2 + b^2 = 15
a
2
+
b
2
=
15
, compute
a
3
+
b
3
a^3 + b^3
a
3
+
b
3
.
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