Art of Problem Solving

2000 AMC 10 Problems/Problem 15: Difference between revisions

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New page: <math>ab=a-b</math> <math>\frac{a}{b}+\frac{b}{a}-ab=\frac{a^2+b^2}{ab}-ab=\frac{-a^2b^2+a^2+b^2}{ab}</math> <math>\frac{-a^2+2ab-b^2+a^2+b^2}{ab}=2</math>. E.
 
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==Problem==
==Solution==
<math>ab=a-b</math>
<math>ab=a-b</math>


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E.
E.
==See Also==
{{AMC10 box|year=2000|num-b=14|num-a=16}}

Revision as of 18:54, 8 January 2009

Problem

Solution

$ab=a-b$

$\frac{a}{b}+\frac{b}{a}-ab=\frac{a^2+b^2}{ab}-ab=\frac{-a^2b^2+a^2+b^2}{ab}$

$\frac{-a^2+2ab-b^2+a^2+b^2}{ab}=2$.

E.

See Also

2000 AMC 10 (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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 10 Problems and Solutions