Difference between revisions of "1958 AHSME Problems/Problem 9"
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== Problem == | == Problem == | ||
| − | A value of <math> x</math> satisfying the equation <math> x^2 | + | A value of <math> x</math> satisfying the equation <math> x^2 + b^2 = (a - x)^2</math> is: |
| − | <math> \textbf{(A)}\ \frac{b^2 | + | <math> \textbf{(A)}\ \frac{b^2 + a^2}{2a}\qquad |
| − | \textbf{(B)}\ \frac{b^2 | + | \textbf{(B)}\ \frac{b^2 - a^2}{2a}\qquad |
| − | \textbf{(C)}\ \frac{a^2 | + | \textbf{(C)}\ \frac{a^2 - b^2}{2a}\qquad |
| − | \textbf{(D)}\ \frac{a | + | \textbf{(D)}\ \frac{a - b}{2}\qquad |
| − | \textbf{(E)}\ \frac{a^2 | + | \textbf{(E)}\ \frac{a^2 - b^2}{2}</math> |
== Solution == | == Solution == | ||
Latest revision as of 22:06, 13 March 2015
Problem
A value of 
satisfying the equation 
is:
Solution
Solve for x:
![\[x^2+b^2=(a-x)^2\]](http://latex.artofproblemsolving.com/6/1/8/618e051c79dcf1343e17838c080fcc19f7dd98f9.png)
![\[x^2+b^2=x^2-2ax+a^2\]](http://latex.artofproblemsolving.com/e/7/6/e760124bbc73451cc04a74284f5ff2f29c2e4f7c.png)
![\[b^2=-2ax+a^2\]](http://latex.artofproblemsolving.com/0/f/2/0f23779400136d4596801721ec63ea4e1afee3d8.png)
![\[2ax=a^2-b^2\]](http://latex.artofproblemsolving.com/2/6/f/26f3ed802b7ad898ac2a2f61ea1d9ced6591f36c.png)
![\[x=\frac{a^2-b^2}{2a} \to \boxed{\text{(C)}}\]](http://latex.artofproblemsolving.com/d/0/e/d0e2e1fb57791129ec18f5cca711cf679045552f.png)
See Also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
