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Difference between revisions of "1966 AHSME Problems/Problem 5"

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Latest revision as of 11:39, 5 July 2013

Problem

The number of values of $x$ satisfying the equation \[\frac {2x^2 - 10x}{x^2 - 5x} = x - 3\] is:

$\text{(A)} \ \text{zero} \qquad \text{(B)} \ \text{one} \qquad \text{(C)} \ \text{two} \qquad \text{(D)} \ \text{three} \qquad \text{(E)} \ \text{an integer greater than 3}$

Solution

Since $x^2 - 5x$ is in the denominator, $x \neq 0,5$. Simplifying,

\[2\left(\frac{x^2 - 5}{x^2 - 5}\right) = 2 = x-3\]

Thus $x = 5$, which isn't in the domain of the equation. Thus there are no values of $x \Rightarrow \mathrm{(A)}$.

See also

1966 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
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
All AHSME Problems and Solutions

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