Difference between revisions of "2024 AIME II Problems/Problem 4"
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<math>-a-b+c = \frac{1}{4}</math> | <math>-a-b+c = \frac{1}{4}</math> | ||
− | Now, we can solve to get <math>a = \frac{-7}{24}, b = \frac{-9}{24}, c = \frac{-5}{12}</math>. Plugging these values in, we obtain <math> | + | Now, we can solve to get <math>a = \frac{-7}{24}, b = \frac{-9}{24}, c = \frac{-5}{12}</math>. Plugging these values in, we obtain <math>|4a + 3b + 2c| = \frac{25}{8} \implies \boxed{033}</math>. ~akliu |
Revision as of 20:03, 8 February 2024
Problem
Let and
be positive real numbers that satisfy the following system of equations:
Then the value of
is
where
and
are relatively prime positive integers. Find
.
Solution 1
Denote ,
, and
.
Then, we have:
Now, we can solve to get . Plugging these values in, we obtain
. ~akliu