Difference between revisions of "2000 AMC 12 Problems/Problem 11"

Revision as of 15:25, 3 January 2008

Two non-zero real numbers, $a$ and $b,$ satisfy $ab = a - b$ . Which of the following is a possible value of $\frac {a}{b} + \frac {b}{a} - ab$ ?

$\text{(A)} \ - 2 \qquad \text{(B)} \ \frac { - 1}{2} \qquad \text{(C)} \ \frac {1}{3} \qquad \text{(D)} \ \frac {1}{2} \qquad \text{(E)} \ 2$

WLOG, let a=1. Solving for b, we have b=1/2, and $\frac {a}{b} + \frac {b}{a} - ab=2\Rightarrow \text{(E)}$

2000 AMC 12 (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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
All AMC 12 Problems and Solutions

@@ Line 5: / Line 5: @@
 ==Solution==
-{{solution}}
+[[WLOG]], let a=1. Solving for b, we have b=1/2, and <math>\frac {a}{b} + \frac {b}{a} - ab=2\Rightarrow \text{(E)}</math>
 ==See Also==
+{{AMC12 box|year=2000|num-b=10|num-a=12}}
+[[Category:Introductory Algebra Problems]]