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 formula|distance]] between those two points is <math>\boxed{\textbf{(C) }\sqrt{2}}</math>. |
==See Also== | ==See Also== |
Latest revision as of 10:10, 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 | |
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All AHSME Problems and Solutions |
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