Difference between revisions of "1958 AHSME Problems/Problem 23"

m (Problem)
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== Solution ==
 
== Solution ==
<math>\fbox{}</math>
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Let us represent the increase or decrease in <math>x</math> by <math>(x \pm a)</math>
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Thus our original expression becomes
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<cmath>(x \pm a)^2 - 3</cmath>
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<cmath>x^2 \pm 2ax + a^2 - 3</cmath>
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The absolute difference between these two expressions is <math>\pm 2ax + a^2</math>
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Therefore, the answer is <math>\fbox{(A) \pm 2ax + a^2}</math>
  
 
== See Also ==
 
== See Also ==

Revision as of 01:59, 22 December 2015

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 $\fbox{(A) \pm 2ax + a^2}$ (Error compiling LaTeX. ! Missing $ inserted.)

See Also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 22
Followed by
Problem 24
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All AHSME Problems and Solutions

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