Difference between revisions of "1951 AHSME Problems/Problem 44"
(Created page with "== Problem == If <math> \frac{xy}{x+y}= a,\frac{xz}{x+z}= b,\frac{yz}{y+z}= c </math>, where <math> a, b, c </math> are other than zero, then <math>x</math> equals: <math> \tex...") |
|||
(2 intermediate revisions by one other user not shown) | |||
Line 16: | Line 16: | ||
A little algebraic manipulation yields that | A little algebraic manipulation yields that | ||
− | <cmath>x=\boxed{\textbf{(E)}\frac{2abc}{ac+bc-ab}</cmath> | + | <cmath>x=\boxed{\textbf{(E)}\ \frac{2abc}{ac+bc-ab}}</cmath> |
== See Also == | == See Also == | ||
Line 22: | Line 22: | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 11:26, 5 July 2013
Problem
If , where
are other than zero, then
equals:
Solution
Note that ,
, and
. Therefore
Therefore
A little algebraic manipulation yields that
See Also
1951 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 43 |
Followed by Problem 45 | |
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.