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Difference between revisions of "2022 AMC 8 Problems/Problem 2"

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==Video Solution==
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https://youtu.be/Ij9pAy6tQSg?t=91
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~Interstigation
  
 
==See Also==  
 
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Revision as of 23:33, 18 February 2022

Problem

Consider these two operations: \begin{align*} a \, \blacklozenge \, b &= a^2 - b^2\\ a \, \bigstar \, b &= (a - b)^2 \end{align*} What is the value of $(5 \, \blacklozenge \, 3) \, \bigstar \, 6?$

$\textbf{(A) } {-}20 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 100 \qquad \textbf{(E) } 220$

Solution

We have \begin{align*} (5 \, \blacklozenge \, 3) \, \bigstar \, 6 &= \left(5^2-3^2\right) \, \bigstar \, 6 \\ &= 16 \, \bigstar \, 6 \\ &= (16-6)^2 \\ &= \boxed{\textbf{(D) } 100}. \end{align*} pog

Video Solution

https://youtu.be/Ij9pAy6tQSg?t=91

~Interstigation

See Also

2022 AMC 8 (Problems • Answer Key • Resources)
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Problem 1 		Followed by
Problem 3
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All AJHSME/AMC 8 Problems and Solutions

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