2020 AMC 10A Problems/Problem 5
Contents
[hide]Problem 5
What is the sum of all real numbers for which
Solution 1
Split the equation into two cases, where the value inside the absolute value is positive and nonpositive.
The first case yields , which is equal to . Therefore, the two values for the positive case is and .
Similarly, taking the nonpositive case for the value inside the absolute value notation yields . Factoring and simplifying gives , so the only value for this case is .
Summing all the values results in .
Solution 2
We have the equations and x^2-12x+36=2$.
Notice that the second is a perfect square with a double root at$ (Error compiling LaTeX. Unknown error_msg)x=61212+6=\boxed{\text{(C) }18}$.
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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