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If set M consists of the root(s) of equation 2-x^2 = (x-2)^2

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If set M consists of the root(s) of equation 2-x^2 = (x-2)^2 [#permalink] New post 19 Nov 2012, 01:49
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If set M consists of the root(s) of 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

M18-36

[Reveal] Spoiler:
I am having trouble with the below question

If set M consists of the root(s) of equation 2−x^2=(x−2)^2, what is the range of set M?

2−x^2=(x−2)^2;

2−x^2=x^2−4x+4; (how do I get from here to the next row?)

x^2−2x+1=0;

(x−1)^2=0;

Thanks,
Jennifer
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Nov 2012, 01:54, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If set M consists of the root(s) of equation 2-x^2 = (x-2)^2 [#permalink] New post 19 Nov 2012, 02:00
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If set M consists of the root(s) of 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 --> add (x^2-2) to both sides: 2-x^2+(x^2-2)=x^2-4x+4+(x^2-2)=0 --> 0=2x^2-4x+2 --> reduce by 2: 0=x^2-2x+1 --> (x-1)^2=0 --> x=1. So, set M consists of only one element.

The range of a single element set is 0.

Answer: A.

Hope it's clear.
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Re: If set M consists of the root(s) of equation 2-x^2 = (x-2)^2 [#permalink] New post 19 Nov 2012, 02:32
thank you, very helpful
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Re: If set M consists of the root(s) of equation 2-x^2 = (x-2)^2 [#permalink] New post 23 Feb 2014, 04:02
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Re: If set M consists of the root(s) of equation 2-x^2 = (x-2)^2   [#permalink] 23 Feb 2014, 04:02
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