a negative value of x

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Jun 18, 2010 4:09 am

For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Problem Solving | Fri Jun 18, 2010 4:09 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Fri Jun 18, 2010 4:12 am

[(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0
If you observe closely, internal bracket turns x^2
so (x^2)^1/2 + 2|X| - 6 = 0

(x^2)^1/2 = x [not -x]

x+2|X| - 6 = 0

if x>0 then |X| = x else -x
assume x>0, then
3x-6 = 0 which gives x = 2

when x<0
-x - 6 = 0
x= -6

question is asking us for negative value so Answer -6

Last edited by kvcpk on Fri Jun 18, 2010 4:19 am, edited 2 times in total.

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Fri Jun 18, 2010 4:15 am

For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

[(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0
[x^2+2x+1 -2x-1]^1/2 + 2|x| - 6 = 0
x+ 2|x| - 6 = 0
this can be written as
x+2x-6=0 x=2
and x-2x-6=0 x=-6

so ans wer will be -6

Ideation without execution is delusion

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singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Sat Jun 19, 2010 12:35 am

amising6 wrote:For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

[(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0
[x^2+2x+1 -2x-1]^1/2 + 2|x| - 6 = 0
x+ 2|x| - 6 = 0
this can be written as
x+2x-6=0 x=2
and x-2x-6=0 x=-6

so ans wer will be -6

how can you put

[(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0 under the same exponential power..what property am i missing here?

(x+1)^2 - (2x+1)^1/2 does not share the same exponent does it?

thanks. Preet.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Jun 19, 2010 12:44 am

singhpreet1 wrote:
amising6 wrote:For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

[(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0
[x^2+2x+1 -2x-1]^1/2 + 2|x| - 6 = 0
x+ 2|x| - 6 = 0
this can be written as
x+2x-6=0 x=2
and x-2x-6=0 x=-6

so ans wer will be -6
how can you put

[(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0 under the same exponential power..what property am i missing here?

(x+1)^2 - (2x+1)^1/2 does not share the same exponent does it?

thanks. Preet.

Hi Preet, your doubt is most welcome. Actually, the exponent Â½ is on the entire [(x + 1) ^2 - (2 x + 1)], which reduces to x^2 bearing an exponent Â½, which is finally x. Rest is already very well explained by amising6 above. It could be the bracket's property that you were missing here. Stay tuned!

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Sat Jun 19, 2010 12:52 am

yea got that..right on Sanju...my bad!

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Sat Jun 19, 2010 12:56 am

singhpreet1 wrote:
amising6 wrote:For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

[(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0
[x^2+2x+1 -2x-1]^1/2 + 2|x| - 6 = 0
x+ 2|x| - 6 = 0
this can be written as
x+2x-6=0 x=2
and x-2x-6=0 x=-6

so ans wer will be -6
how can you put

[(x + 1) ^2 - (2 x + 1)] ^Â½ + 2|x| - 6 = 0 under the same exponential power..what property am i missing here?

(x+1)^2 - (2x+1)^1/2 does not share the same exponent does it?

thanks. Preet.

[(x + 1) ^2 - (2 x + 1)] ^Â½

[(x + 1) ^2 - (2 x + 1)] this whole is raised to power 1/2

Ideation without execution is delusion

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mj78ind: Master | Next Rank: 500 Posts; Posts: 265; Joined: Mon Dec 28, 2009 9:45 pmFollowed by: 2 members; Thanked: 26 times; GMAT Score:760

by mj78ind » Sat Jun 19, 2010 1:02 am

sqrt((x+1)^2-(2x+1)) + 2abs(x) - 6 =0

gives abs(x) + 2abs(x) - 6 =0

which is 3abs(x) = 6 or abs(x) = 2

Hence x = -2

Answer D

OA pls?

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