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2020 LMT Spring
8
8
Part of
2020 LMT Spring
Problems
(1)
Spring 2020 Team Round Problem 8
Source:
8/22/2020
Let
a
,
b
a,b
a
,
b
be real numbers satisfying
a
2
+
b
2
=
3
a
b
=
75
a^{2} + b^{2} = 3ab = 75
a
2
+
b
2
=
3
ab
=
75
and
a
>
b
a>b
a
>
b
. Compute
a
3
ā
b
3
a^{3}-b^{3}
a
3
ā
b
3
.