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2017 Purple Comet Problems
20
Purple Comet 2017 HS problem 20
Purple Comet 2017 HS problem 20
Source:
March 19, 2020
algebra
Problem Statement
Let
a
a
a
be a solution to the equation
x
2
+
2
=
x
3
+
45
3
\sqrt{x^2 + 2} = \sqrt[3]{x^3 + 45}
x
2
+
2
=
3
x
3
+
45
. Evaluate the ratio of
2017
a
2
\frac{2017}{a^2}
a
2
2017
to
a
2
−
15
a
+
2
a^2 - 15a + 2
a
2
−
15
a
+
2
.
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