Difference between revisions of "1958 AHSME Problems/Problem 11"
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==Problem== | ==Problem== | ||
| − | The number of roots satisfying the equation <math> \sqrt{5 | + | The number of roots satisfying the equation <math> \sqrt{5 - x} = x\sqrt{5 - x}</math> is: |
<math> \textbf{(A)}\ \text{unlimited}\qquad | <math> \textbf{(A)}\ \text{unlimited}\qquad | ||
| Line 8: | Line 8: | ||
\textbf{(D)}\ 1\qquad | \textbf{(D)}\ 1\qquad | ||
\textbf{(E)}\ 0</math> | \textbf{(E)}\ 0</math> | ||
| − | |||
==Solution== | ==Solution== | ||
Latest revision as of 22:09, 13 March 2015
Problem
The number of roots satisfying the equation 
is:
Solution
Solve the equation for x.
![\[\sqrt{5-x}=x\sqrt{5-x}\]](http://latex.artofproblemsolving.com/9/e/b/9eb677a3a1cdce8abab1212879da057d0e10dec6.png)
![\[x\sqrt{5-x} - \sqrt{5-x} = 0\]](http://latex.artofproblemsolving.com/7/4/f/74f4d326a19ee05f0adaf0831356a5b28f458b3b.png)
![\[(x-1)\sqrt{5-x}=0\]](http://latex.artofproblemsolving.com/f/3/6/f364ac167577eed167f1b2b68e59f5885b7acdf3.png)
![\[x=1,5\]](http://latex.artofproblemsolving.com/3/6/9/36955b9956dc494c6d768c67397162bd5c111ac6.png)
There are two solutions 
See also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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. 
