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Difference between revisions of "2021 Fall AMC 12B Problems/Problem 7"

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==Solution 1 (Bash) ==
  
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Just plug in all these options one by one, and one sees that all but <math>D</math> fails to satisfy the equation.
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For <math>D</math>, substitute <math>z=x</math> and <math>y=x+1</math>:
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<math>LHS=x(x-(x+1))+(x+1)(x+1-x)+x(x-x)=(-x)+(x+1)=1=RHS</math>
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Hence the answer is <math>\boxed{\textbf{(D)}}.</math>

Revision as of 22:27, 23 November 2021

Solution 1 (Bash)

Just plug in all these options one by one, and one sees that all but $D$ fails to satisfy the equation.

For $D$, substitute $z=x$ and $y=x+1$:

$LHS=x(x-(x+1))+(x+1)(x+1-x)+x(x-x)=(-x)+(x+1)=1=RHS$

Hence the answer is $\boxed{\textbf{(D)}}.$

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