Bunuel wrote:
What is the range of the roots of \(||x – 1| – 2| = 1\)?
A. 0
B. 2
C. 4
D. 6
E. 8
Another approach
Let\(z = x -1\)
\(||z| – 2| = 1\) .............square bothsides
\(z^2-4|z|+4=1\)
\(z^2-4|z|+3=0\)
\((|z|-3)(|z|-1)=0\)
\(|z|=3\) or\(|z|=1\)
substitute z from above
\(x–1=3\) or \(x–1=-3\)
\(x=4\) or \(x=-2\)
OR
\(x–1=1\) or \(x–1=-1\)
\(x=2\) or \(x=0\)
Range = Max value - min value
\(R=4-(-2)=4+2=6\)
Answer: D
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