Difference between revisions of "2022 AMC 10A Problems/Problem 6"
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The only answer choice equal to <math>5</math> for <math>a=-1</math> is <math>A</math>, so the answer is <math>\boxed{\textbf{(A) } 3-2a}.</math> | The only answer choice equal to <math>5</math> for <math>a=-1</math> is <math>A</math>, so the answer is <math>\boxed{\textbf{(A) } 3-2a}.</math> | ||
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-MathWizard09 | -MathWizard09 | ||
Revision as of 01:48, 12 November 2022
Contents
Problem
Which expression is equal to ![\[\left|a-2-\sqrt{(a-1)^2}\right|\]](http://latex.artofproblemsolving.com/9/8/4/984209dd4e5f26c2736cb3fd5c2248f83f75fd36.png)
for 
Solution
We have
~MRENTHUSIASM
Solution 2
WLOG, assume 
Then, the given expression simplifies to 
:
![\[\left|a-2-\sqrt{(a-1)^2}\right| = \left|-1-2-\sqrt{(-1-1)^2}\right| = \left|-1-2-\sqrt{4}\right| = \left|-1-2-2\right| = 5.\]](http://latex.artofproblemsolving.com/4/8/e/48e14b1c3c20ee4dffe1af824ccdd06bec3df92c.png)
Then, we test each of the answer choices to see which one is equal to :
The only answer choice equal to for 
is 
, so the answer is 
-MathWizard09
See Also
| 2022 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
