1958 AHSME Problems/Problem 9
Problem
A value of 
satisfying the equation $x^2 \plus{} b^2 \equal{} (a \minus{} x)^2$ (Error compiling LaTeX. Unknown error_msg) is:
$\textbf{(A)}\ \frac{b^2 \plus{} a^2}{2a}\qquad \textbf{(B)}\ \frac{b^2 \minus{} a^2}{2a}\qquad \textbf{(C)}\ \frac{a^2 \minus{} b^2}{2a}\qquad \textbf{(D)}\ \frac{a \minus{} b}{2}\qquad \textbf{(E)}\ \frac{a^2 \minus{} b^2}{2}$ (Error compiling LaTeX. Unknown error_msg)
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 AHSME (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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
