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24 November, 13:08

If x=7+root 40, find the value of root x+1by the root of x

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  1. 24 November, 13:10
    0
    Chapter : Algebra

    Study : Math in Junior high school

    x = 7 + √40

    find √x of √x + 1

    = √x + 1

    = √ (7+√40) + 1

    in Formula is:

    = √7+√40 = √x + √y

    = (√7+√40) ² = (√x + √y) ²

    = 7+√40 = x + 2√xy + y

    = 7 + √40 = x + y + 2√xy

    → 7 = x + y → y = 7 - x ... Equation 1

    → √40 = 2√xy → √40 = 2.2√10 = 4√10

    = xy = 10 ... Equation 2

    substitution Equation 1 to 2:

    = xy = 10

    = x (7-x) = 10

    = 7x - x² = 10

    = x² - 7x + 10 = 0

    = (x - 5) (x - 2) = 0

    = x = 5 or x = 2

    Subsitution x = 5 and x = 2, to equation 1

    #For x = 5

    = y = 7 - x

    = y = 7 - (5)

    = y = 2

    #For x = 2

    = y = 7 - x

    = y = 7 - (2)

    = y = 5

    and his x and y was find:

    #Equation 1:

    = x = 5 and y = 2

    #Equation 2:

    = x = 2 and y = 5

    So that:

    √7+√40 = √x + √y

    = √7+√40 = √2 + √5

    And that is answer of question:

    = √2 + √5 + 1
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