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Difference between revisions of "2025 AMC 8 Problems/Problem 1"

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Let m and n be 2 integers such that m <math>></math> n. Suppose m + n = 20, <math>m^2</math> + <math>n^2</math> = 328, find <math>m^2</math> - <math>n^2</math>.
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Let <math>m</math> and <math>n</math> be <math>2</math> integers such that <math>m>n</math>. Suppose <math>m+n=20</math>, <math>m^2+n^2=328</math>, find <math>m^2-n^2</math>.
  
 
<math>\textbf{(A)}\ 280 \qquad \textbf{(B)}\ 292 \qquad \textbf{(C)}\ 300 \qquad \textbf{(D)}\ 320 \qquad \textbf{(E)}\ 340</math>
 
<math>\textbf{(A)}\ 280 \qquad \textbf{(B)}\ 292 \qquad \textbf{(C)}\ 300 \qquad \textbf{(D)}\ 320 \qquad \textbf{(E)}\ 340</math>

Revision as of 07:35, 18 February 2024

Let $m$ and $n$ be $2$ integers such that $m>n$. Suppose $m+n=20$, $m^2+n^2=328$, find $m^2-n^2$.

$\textbf{(A)}\ 280 \qquad \textbf{(B)}\ 292 \qquad \textbf{(C)}\ 300 \qquad \textbf{(D)}\ 320 \qquad \textbf{(E)}\ 340$

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