Difference between revisions of "1955 AHSME Problems/Problem 47"
Coolmath34 (talk | contribs) (Created page with "== Problem 47== The expressions <math>a+bc</math> and <math>(a+b)(a+c)</math> are: <math> \textbf{(A)}\ \text{always equal}\qquad\textbf{(B)}\ \text{never equal}\qquad\text...") |
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<cmath>a + bc = a^2 + ab + ac + bc</cmath> | <cmath>a + bc = a^2 + ab + ac + bc</cmath> | ||
<cmath>a = a^2 + ab + ac</cmath> | <cmath>a = a^2 + ab + ac</cmath> | ||
| − | These expressions are | + | <cmath>a((a + b + c) - 1) = 0</cmath> |
| + | These expressions are <math>\boxed{\text{(C) equal whenever } a + b + c = 1.}</math> | ||
== See Also == | == See Also == | ||
Latest revision as of 19:54, 24 July 2022
Problem 47
The expressions 
and 
are:
Solution
Using the FOIL method, we see that 
We want to solve
![\[a + bc = a^2 + ab + ac + bc\]](http://latex.artofproblemsolving.com/a/f/8/af89451fb95b007c0e1b818bbd1e731e4fd3c4ca.png)
![\[a = a^2 + ab + ac\]](http://latex.artofproblemsolving.com/c/b/9/cb962b5fd7e5bafc60073f5ce11e627efd515cfb.png)
![\[a((a + b + c) - 1) = 0\]](http://latex.artofproblemsolving.com/1/e/b/1ebfb677c15ebb23ecf48b4cad4b0d3052946d9d.png)
These expressions are 
See Also
| 1955 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 46 |
Followed by Problem 48 | |
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| All AHSME Problems and Solutions | ||
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