Difference between revisions of "1957 AHSME Problems/Problem 23"
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We can merge the two equations to create <math>x^2+y=x+y</math>. Using either the quadratic equation or factoring, we get two solutions with <math>x</math>-coordinates <math>0</math> and <math>1</math>. | We can merge the two equations to create <math>x^2+y=x+y</math>. Using either the quadratic equation or factoring, we get two solutions with <math>x</math>-coordinates <math>0</math> and <math>1</math>. | ||
| − | Plugging this into either of the original equations, we get <math>(0,10)</math> and <math>(1,9)</math>. The distance between those two points is <math>\boxed{\textbf{(C) }\sqrt{2}}</math> | + | Plugging this into either of the original equations, we get <math>(0,10)</math> and <math>(1,9)</math>. The distance between those two points is <math>\boxed{\textbf{(C) }\sqrt{2}}</math>. |
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==See Also== | ==See Also== | ||
{{AHSME 50p box|year=1957|num-b=22|num-a=24}} | {{AHSME 50p box|year=1957|num-b=22|num-a=24}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:AHSME]][[Category:AHSME Problems]] | [[Category:AHSME]][[Category:AHSME Problems]] | ||
Revision as of 09:09, 25 July 2024
The graph of 
and the graph of 
meet in two points. The distance between these two points is:
Solution
We can merge the two equations to create 
. Using either the quadratic equation or factoring, we get two solutions with 
-coordinates 
and 
.
Plugging this into either of the original equations, we get 
and 
. The distance between those two points is 
.
See Also
| 1957 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
| 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. 
