1958 AHSME Problems/Problem 23

Problem

If, in the expression $x^2 - 3$ , $x$ increases or decreases by a positive amount of $a$ , the expression changes by an amount:

$\textbf{(A)}\ {\pm 2ax + a^2}\qquad \textbf{(B)}\ {2ax \pm a^2}\qquad \textbf{(C)}\ {\pm a^2 - 3} \qquad \textbf{(D)}\ {(x + a)^2 - 3}\qquad\\ \textbf{(E)}\ {(x - a)^2 - 3}$

Solution

Let us represent the increase or decrease in $x$ by $(x \pm a)$

Thus our original expression becomes $(x \pm a)^2 - 3$ $x^2 \pm 2ax + a^2 - 3$ The absolute difference between these two expressions is $\pm 2ax + a^2$ .

Therefore, the answer is $\fbox{(A)}$

1958 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 22	Followed by Problem 24
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1958 AHSME Problems/Problem 23

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