# 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...") |
Whirltwister (talk | contribs) (→Solutions) |
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<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 17:44, 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. ! Undefined control sequence.)

## 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