Difference between revisions of "2006 AMC 12A Problems/Problem 11"
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== Problem == | == Problem == | ||
| − | Which of the following describes the graph of the equation <math>(x+y)^2=x^2+y^2</math>? | + | Which of the following describes the [[graph]] of the equation <math>(x+y)^2=x^2+y^2</math>? |
<math> \mathrm{(A) \ } \;\mathrm{the\; empty\; set}\;\qquad \mathrm{(B) \ } \;\mathrm{one\; point}</math><math>\mathrm{(C) \ } \;\mathrm{two\; lines}\;\qquad \mathrm{(D) \ } \;\mathrm{a\; circle}</math><math>\mathrm{(E) \ } \;\mathrm{the\; entire \; plane}\;</math> | <math> \mathrm{(A) \ } \;\mathrm{the\; empty\; set}\;\qquad \mathrm{(B) \ } \;\mathrm{one\; point}</math><math>\mathrm{(C) \ } \;\mathrm{two\; lines}\;\qquad \mathrm{(D) \ } \;\mathrm{a\; circle}</math><math>\mathrm{(E) \ } \;\mathrm{the\; entire \; plane}\;</math> | ||
== Solution == | == Solution == | ||
| − | <math> (x+y)^2 = x^2 + y^2 </math> | + | <math> (x+y)^2=x^2+y^2 </math> |
<math> x^2 + 2xy + y^2 = x^2 + y^2 </math> | <math> x^2 + 2xy + y^2 = x^2 + y^2 </math> | ||
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<math> 2xy = 0 </math> | <math> 2xy = 0 </math> | ||
| − | Either | + | Either <math> x = 0 </math> or <math> y = 0 </math>. The [[union]] of them is 2 lines <math> \Rightarrow C</math>. |
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== See also == | == See also == | ||
* [[2006 AMC 12A Problems]] | * [[2006 AMC 12A Problems]] | ||
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| − | + | {{AMC box|year=2006|n=12A|num-b=10|num-a=12}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 19:44, 31 January 2007
Problem
Which of the following describes the graph of the equation 
?
Solution
Either 
or 
. The union of them is 2 lines 
.
See also
| {{{header}}} | ||
| Preceded by Problem 10 |
AMC 12A 2006 |
Followed by Problem 12 |
