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2020 MOAA
TO5
TO5
Part of
2020 MOAA
Problems
(1)
2020 MOAA Theme Optimization TO 5
Source:
1/23/2022
For a real number
x
x
x
, the minimum value of the expression
2
x
2
+
x
−
3
x
2
−
2
x
+
3
\frac{2x^2 + x - 3}{x^2 - 2x + 3}
x
2
−
2
x
+
3
2
x
2
+
x
−
3
can be written in the form
a
−
b
c
\frac{a-\sqrt{b}}{c}
c
a
−
b
, where
a
,
b
a, b
a
,
b
, and
c
c
c
are positive integers such that
a
a
a
and
c
c
c
are relatively prime. Find
a
+
b
+
c
a + b + c
a
+
b
+
c
algebra
theme
2020