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If x<0, which of the following must be true? [#permalink]

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27 Dec 2017, 07:20

Bunuel wrote:

If x < 0, which of the following must be true?

I. \(x<\sqrt{−x}\)

II. \(x^2>\sqrt{x^2}\)

III. \(x=−\sqrt{x^2}\)

A. I only B. I and II only C. I and III only D. I, II, and III E. None of the above

Bunuel please correct me if i am wrong isn't \sqrt{x} =|x|

and if it is then by that logic how is this statement correct \(x<\sqrt{−x}\)

BunuelVeritasPrepKarishma I am pretty sure i have seen you guys using \sqrt{x} =|x| in answers . Then please tell me how can statement 1 be correct thank you

If x<0, which of the following must be true? [#permalink]

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27 Dec 2017, 07:26

Ravindra.here wrote:

Bunuel wrote:

If x < 0, which of the following must be true?

I. \(x<\sqrt{−x}\)

II. \(x^2>\sqrt{x^2}\)

III. \(x=−\sqrt{x^2}\)

A. I only B. I and II only C. I and III only D. I, II, and III E. None of the above

Bunuel please correct me if i am wrong isn't \sqrt{x} =|x|

and if it is then by that logic how is this statement correct \(x<\sqrt{−x}\)

BunuelVeritasPrepKarishma I am pretty sure i have seen you guys using \sqrt{x} =|x| in answers . Then please tell me how can statement 1 be correct thank you

If x<0, which of the following must be true? [#permalink]

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27 Dec 2017, 08:16

niks18 wrote:

Ravindra.here wrote:

Bunuel wrote:

If x < 0, which of the following must be true?

I. \(x<\sqrt{−x}\)

II. \(x^2>\sqrt{x^2}\)

III. \(x=−\sqrt{x^2}\)

A. I only B. I and II only C. I and III only D. I, II, and III E. None of the above

Bunuel please correct me if i am wrong isn't \sqrt{x} =|x|

and if it is then by that logic how is this statement correct \(x<\sqrt{−x}\)

BunuelVeritasPrepKarishma I am pretty sure i have seen you guys using \sqrt{x} =|x| in answers . Then please tell me how can statement 1 be correct thank you

The question mentions that \(x<0\) i.e negative so \(-x\) will be positive

if \(x=-3\), then \(-x=-(-3)=3\)

so \(x<\sqrt{-x}\) is possible

Hi niks18 my confusion is this one \sqrt{-x} is positive here and as \sqrt{x}=|x| here \sqrt{-x} = |-x|=|x| now lets take x=-9 Therefore \sqrt{-x}= |3| this means now two values 3 and -3 Here for both values \(x<\sqrt{−x}\) but what if i take x=-1/4 now \sqrt{-x}= |-1/2|=|1/2| this yeilds two values again

A. I only B. I and II only C. I and III only D. I, II, and III E. None of the above

Bunuel please correct me if i am wrong isn't \sqrt{x} =|x|

and if it is then by that logic how is this statement correct \(x<\sqrt{−x}\)

BunuelVeritasPrepKarishma I am pretty sure i have seen you guys using \sqrt{x} =|x| in answers . Then please tell me how can statement 1 be correct thank you

The red part is not correct.

\(\sqrt{x^2}=|x|\), NOT \(\sqrt{x}=|x|\).

Next, \(x<\sqrt{−x}\) is correct because \((x=negative)<(\sqrt{−x}=\sqrt{positive}=positive)\)

Re: If x<0, which of the following must be true? [#permalink]

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27 Dec 2017, 08:33

Ravindra.here wrote:

Hi niks18 my confusion is this one \sqrt{-x} is positive here and as \sqrt{x}=|x| here \sqrt{-x} = |-x|=|x| now lets take x=-9 Therefore \sqrt{-x}= |3| this means now two values 3 and -3 Here for both values \(x<\sqrt{−x}\) but what if i take x=-1/4 now \sqrt{-x}= |-1/2|=|1/2| this yeilds two values again