Difference between revisions of "2020 AMC 10B Problems/Problem 9"
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==Video Solution== | ==Video Solution== | ||
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+ | ~IceMatrix | ||
==See Also== | ==See Also== |
Revision as of 20:15, 7 February 2020
Contents
Problem
How many ordered pairs of integers satisfy the equation
Solution
Rearranging the terms and and completing the square for yields the result
. Then, notice that
can only be
,
and
because any value of
that is greater than 1 will cause the term
to be less than
, which is impossible as
must be real. Therefore, plugging in the above values for
gives the ordered pairs
,
,
, and
gives a total of
ordered pairs.
Video Solution
~IceMatrix
See Also
2020 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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