Difference between revisions of "2006 AMC 10B Problems/Problem 7"

Revision as of 21:54, 7 September 2011

Problem

Which of the following is equivalent to $\sqrt{\frac{x}{1-\frac{x-1}{x}}}$ when $x < 0$ ?

$\mathrm{(A) \ } -x\qquad \mathrm{(B) \ } x\qquad \mathrm{(C) \ } 1\qquad \mathrm{(D) \ } \sqrt{\frac{x}{2}}\qquad \mathrm{(E) \ } x\sqrt{-1}$

Solution

$\sqrt{\frac{x}{1-\frac{x-1}{x}}} = \sqrt{\frac{x}{\frac{x}{x}-\frac{x-1}{x}}} = \sqrt{\frac{x}{\frac{x-(x-1)}{x}}} = \sqrt{\frac{x}{\frac{1}{x}}} = \sqrt{x^2} = |x|$

Since $x<0$

$|x|= -x \Rightarrow A$

2006 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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

@@ Line 12: / Line 12: @@
 == See Also ==
-*[[2006 AMC 10B Problems]]
+{{AMC10 box|year=2006|ab=B|num-b=6|num-a=8}}
-*[[2006 AMC 10B Problems/Problem 6|Previous Problem]]
-*[[2006 AMC 10B Problems/Problem 8|Next Problem]]
 [[Category:Introductory Algebra Problems]]

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Difference between revisions of "2006 AMC 10B Problems/Problem 7"

Revision as of 21:54, 7 September 2011

Problem

Solution

See Also