a negative value of x

[(x + 1) ^2 - (2 x + 1)] ^½ + 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

For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

[(x + 1) ^2 - (2 x + 1)] ^½ + 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

amising6 wrote:For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

[(x + 1) ^2 - (2 x + 1)] ^½ + 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)] ^½ + 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.

singhpreet1 wrote:

amising6 wrote:For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

[(x + 1) ^2 - (2 x + 1)] ^½ + 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)] ^½ + 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 ½ is on the entire [(x + 1) ^2 - (2 x + 1)], which reduces to x^2 bearing an exponent ½, 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!

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

singhpreet1 wrote:

amising6 wrote:For which of a negative value of x the relation [(x + 1) ^2 - (2 x + 1)] ^½ + 2|x| - 6 = 0 is true?
(A) -5
(B) -4
(C) -3
(D) -2
(E) -1

[(x + 1) ^2 - (2 x + 1)] ^½ + 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)] ^½ + 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)] ^½


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

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?