Difference between revisions of "1958 AHSME Problems/Problem 11"

m (See also)
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==Problem==
 
==Problem==
  
The number of roots satisfying the equation <math> \sqrt{5 \minus{} x} \equal{} x\sqrt{5 \minus{} x}</math> is:
+
The number of roots satisfying the equation <math> \sqrt{5 - x} = x\sqrt{5 - x}</math> is:
  
 
<math> \textbf{(A)}\ \text{unlimited}\qquad  
 
<math> \textbf{(A)}\ \text{unlimited}\qquad  
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\textbf{(D)}\ 1\qquad  
 
\textbf{(D)}\ 1\qquad  
 
\textbf{(E)}\ 0</math>
 
\textbf{(E)}\ 0</math>
 
  
 
==Solution==
 
==Solution==

Latest revision as of 23:09, 13 March 2015

Problem

The number of roots satisfying the equation $\sqrt{5 - x} = x\sqrt{5 - x}$ is:

$\textbf{(A)}\ \text{unlimited}\qquad  \textbf{(B)}\ 3\qquad  \textbf{(C)}\ 2\qquad  \textbf{(D)}\ 1\qquad  \textbf{(E)}\ 0$

Solution

Solve the equation for x.

\[\sqrt{5-x}=x\sqrt{5-x}\]

\[x\sqrt{5-x} - \sqrt{5-x} = 0\]

\[(x-1)\sqrt{5-x}=0\]

\[x=1,5\]

There are two solutions $\to \boxed{\textbf{(C)}}$


See also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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All AHSME Problems and Solutions

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