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voodoo_child GMAT Destroyer! Default Avatar
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Need expert help Post Mon Apr 30, 2012 7:40 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    Find the solution of Sqrt(2+sqrt(2+sqrt(2+sqrt(.........

    Here's what I did:

    sqrt(2+x)=x
    Therefore, 2+x=x^2
    Therefore, x^2 - x - 2 => (x-2) (x+1)=0
    X = 2 or -1.

    Correct answer is 2; I am not able to rule out (-1). Any help? Thanks

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    aneesh.kg GMAT Destroyer!
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    Post Mon Apr 30, 2012 7:43 am
    Square root of any quantity is always positive.
    Since x is square root of a quantity here, the negative value (-1) is ruled out.

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    Brent@GMATPrepNow GMAT Instructor
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    Post Mon Apr 30, 2012 9:00 am
    voodoo_child wrote:
    Find the solution of Sqrt(2+sqrt(2+sqrt(2+sqrt(.........

    Here's what I did:

    sqrt(2+x)=x
    Therefore, 2+x=x^2
    Therefore, x^2 - x - 2 => (x-2) (x+1)=0
    X = 2 or -1.
    Correct answer is 2; I am not able to rule out (-1). Any help? Thanks
    When you solve a question involving square roots, you should plug in the answers to check for extraneous roots (aka, solutions that don't work).

    x=2: sqrt(2+2)=2 (WORKS)
    x=-1: sqrt(2+(-1))=-1 (DOESN'T WORK)

    Cheers,
    Brent

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    voodoo_child GMAT Destroyer! Default Avatar
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    Post Mon Apr 30, 2012 12:06 pm
    Brent@GMATPrepNow wrote:
    x=2: sqrt(2+2)=2 (WORKS)
    x=-1: sqrt(2+(-1))=-1 (DOESN'T WORK)

    Cheers,
    Brent
    Brent and Aneesh - question - Sqrt (1) is not equal to -1? Why? (-1)^2 =1. Therefore, Sqrt(1) = 1 or -1. Correct?

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    Brent@GMATPrepNow GMAT Instructor
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    Post Mon Apr 30, 2012 12:13 pm
    voodoo_child wrote:
    Brent@GMATPrepNow wrote:
    x=2: sqrt(2+2)=2 (WORKS)
    x=-1: sqrt(2+(-1))=-1 (DOESN'T WORK)

    Cheers,
    Brent
    Brent and Aneesh - question - Sqrt (1) is not equal to -1? Why? (-1)^2 =1. Therefore, Sqrt(1) = 1 or -1. Correct?
    By definition, sqrt(n) denotes the positive number whose square is n.
    Similarly, -sqrt(n) denotes the negative number whose square is n.

    So, the takeaway here is that the equation x^2 = 9 has 2 solutions (x = 3, -3), while the equation sqrt(9)= x has only 1 solution (x = 3)

    Cheers,
    Brent

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    2) Calculating combinations in your head
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    aneesh.kg GMAT Destroyer!
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    Post Mon Apr 30, 2012 12:44 pm
    By definition, when the symbol of 'square root' is placed over a quantity, the output must be positive. Notice that you don't get two values when you take the square root of a number on your calculator.

    To clear your confusion, let's take this example:

    say x^2 = 9
    Step1: x = +/- sqrt(9)
    Step2: Since sqrt(9) = 3,
    Step3: x = +/- 3

    So,
    (i) if x^2 = any number, we get two values - one positive and one negative - of x
    (ii) if x = sqrt(number), we get just one positive value of x

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