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16 Sep 2014, 01:04
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If set \(M\) consists of the root(s) of the equation \(2-x^2 = (x-2)^2\), what is the range of set \(M\)?
A. 0
B. \(\frac{1}{\sqrt{2}}\)
C. 1
D. \(\sqrt{2}\)
E. 2
A. 0
B. \(\frac{1}{\sqrt{2}}\)
C. 1
D. \(\sqrt{2}\)
E. 2
16 Sep 2014, 01:05
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Official Solution:
If set \(M\) consists of the root(s) of the equation \(2-x^2 = (x-2)^2\), what is the range of set \(M\)?
A. 0
B. \(\frac{1}{\sqrt{2}}\)
C. 1
D. \(\sqrt{2}\)
E. 2
\(2-x^2 = (x-2)^2\);
\(2-x^2=x^2-4x+4\);
\(x^2-2x+1=0\);
\((x-1)^2=0\);
\(x=1\).
Therefore, set \(M\) contains only one element.
The range of a single element set is 0.
Answer: A
If set \(M\) consists of the root(s) of the equation \(2-x^2 = (x-2)^2\), what is the range of set \(M\)?
A. 0
B. \(\frac{1}{\sqrt{2}}\)
C. 1
D. \(\sqrt{2}\)
E. 2
\(2-x^2 = (x-2)^2\);
\(2-x^2=x^2-4x+4\);
\(x^2-2x+1=0\);
\((x-1)^2=0\);
\(x=1\).
Therefore, set \(M\) contains only one element.
The range of a single element set is 0.
Answer: A
01 Oct 2023, 10:17
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
