Difference between revisions of "2012 AMC 10B Problems/Problem 8"
m (Created page with "== Problem 8 == What is the sum of all integer solutions to <math>1<(x-2)^2<25</math>? <math> \textbf{(A)}\ 10\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 15\qquad\textbf{(D)}\ 19...") |
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| Line 22: | Line 22: | ||
<math>(x-2)^2=4</math> | <math>(x-2)^2=4</math> | ||
| − | <math>x=4</math> | + | <math>x=4,0</math> |
and | and | ||
| Line 28: | Line 28: | ||
<math>(x-2)^2=9</math> | <math>(x-2)^2=9</math> | ||
| − | <math>x=5</math> | + | <math>x=5,-1</math> |
and | and | ||
| Line 34: | Line 34: | ||
<math>(x-2)^2=16</math> | <math>(x-2)^2=16</math> | ||
| − | <math>x=6</math> | + | <math>x=6,-2</math> |
''What is the sum of all integer solutions'' | ''What is the sum of all integer solutions'' | ||
| − | <math>4+5+6=\boxed{ | + | <math>4+5+6+0+(-1)+(-2)=\boxed{12}</math> |
OR | OR | ||
| − | <math> \textbf{( | + | <math> \textbf{(B)}</math> |
Revision as of 18:44, 24 February 2012
Problem 8
What is the sum of all integer solutions to 
?
$\textbf{(A)}\ 10\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 15\qquad\textbf{(D)}\ 19\qquad\textbf{(E)}\25$ (Error compiling LaTeX. Unknown error_msg)
Solutions
= perfect square.
1< perfect square< 25
Perfect square can equal: 4, 9, or 16
Solve for x:
and
and
What is the sum of all integer solutions
OR
