If set M consists of the root(s) of equation 2-x^2 = (x-2)^2 : GMAT Problem Solving (PS)
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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]

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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]

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19 Nov 2012, 02:00
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Expert's post
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.

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]

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19 Nov 2012, 02:32
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Re: If set M consists of the root(s) of equation 2-x^2 = (x-2)^2 [#permalink]

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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]

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01 Jan 2017, 13:11
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If set M consists of the root(s) of equation 2-x^2 = (x-2)^2   [#permalink] 01 Jan 2017, 13:11
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