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# What is the value of sqrt(x^2 - 6x + 9) +sqrt(2-x) + (x- 3),

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Director
Joined: 14 Jan 2007
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What is the value of sqrt(x^2 - 6x + 9) +sqrt(2-x) + (x- 3), [#permalink]  29 May 2007, 09:44
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What is the value of sqrt(x^2 - 6x + 9) +sqrt(2-x) + (x- 3), assuming all terms are well defined.

1. sqrt(2-x)
2. 2x-6 + sqrt(2-x)
3. sqrt(2-x) + x-3
4. 2x-6 + sqrt(x-2)
5. x +sqrt(2-x)

Last edited by vshaunak@gmail.com on 29 May 2007, 09:56, edited 1 time in total.
Director
Joined: 14 Jan 2007
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Hayabusa wrote:
is it 4?

Please do it again as I have edited the choice 4. I think you mean choice 2?
Director
Joined: 30 Nov 2006
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sqrt{x^2 -6x + 9} = sqrt{(x-3)^2} = x-3
so the total value is (x-3) + (x-3) + sqrt{2-x} = 2x-6 + sqrt{2-x}

Director
Joined: 14 Jan 2007
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OA is 1.

as 2-x should be > 0
x < 2

sqrt(x^2-6x+9) = -(x-3) as x-3 < 0
so the value of expression is sqrt(2-x)
CEO
Joined: 17 May 2007
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Hi vishaunak

I follow ur logic where x < 2 and that x-3 by that logic is negative. But how does that lead to answer choice A ? Please clarify ?
Director
Joined: 14 Jan 2007
Posts: 780
Followers: 2

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bsd_lover wrote:
Hi vishaunak

I follow ur logic where x < 2 and that x-3 by that logic is negative. But how does that lead to answer choice A ? Please clarify ?

expression = sqrt(x^2 - 6x + 9) +sqrt(2-x) + (x- 3)
= -(x-3) + sqrt(2-x) + (x-3)
= sqrt(2-x)
I think it should be clear now.
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