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    wearepink's Avatar
    wearepink Posts: 2, Reputation: 1
    New Member
     
    #1

    Dec 25, 2005, 05:51 PM
    squaring both sides twice
    Here's a problem I am having troubles with.

    _ ____
    √x + √x 5 = 5

    Can someone help show me how to solve this?

    Thanks,
    B
    CaptainForest's Avatar
    CaptainForest Posts: 3,645, Reputation: 393
    Ultra Member
     
    #2

    Dec 25, 2005, 11:37 PM
    √x + √x 5 = 5

    Note that √x is also equal to x^1/2

    Therefore,

    √x + √x 5 = 5
    √x + √x = 5 + 5
    2 √x = 10

    √x = 10 / 2
    √x = 5
    x = 5^2/1
    x = 25

    Therefore, x=25

    And a check,
    √x + √x 5 = 5
    √25 + √25 5 = 5
    5 + 5 - 5 = 5... Yes

    Therefore, x=25
    wearepink's Avatar
    wearepink Posts: 2, Reputation: 1
    New Member
     
    #3

    Dec 29, 2005, 07:06 AM
    Squaring both sides twice - quadratic
    Thanks for your help. When I posted my initial message it didn't post right. I am working on quadratic equations so I should wind up with x = ? Two times. The equation should be:

    ._.. . _____.
    √x + √x 5 = 5

    Where the x - 5, not just the x, is under the square root symbol.

    Thanks,
    B
    reinsuranc's Avatar
    reinsuranc Posts: 92, Reputation: 6
    Junior Member
     
    #4

    Jan 5, 2006, 12:17 AM
    x^.5 + (x-5)^.5 = 5
    It is easier to write such equations on this board as x^.5 + (x-5)^.5 = 5, instead of trying to draw square root symbols.

    The answer to the above is 9:

    x^.5 + (x-5)^.5 = 5

    (x^.5 - 5)^2 = ( (x-5)^.5 )^2

    x - 10x^.5 + 25 = x - 5

    Let y = x^.5

    y^2 - 10y + 25 = y^2 - 5

    30 = 10y

    y = 3

    3 = x^.5

    9 = x

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