Divide 27 into two parts such that the sum of their reciprocal is 3 /10

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Divide 27 into two parts such that the sum of their reciprocal is 3 /10

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Everleigh 3 weeks 2021-11-07T00:46:06+00:00 1 Answer 0 views 0

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    2021-11-07T00:47:13+00:00

    Answer:

    Approximately 23 and 4 ( I think the sum of reciprocal is 3/20 and not 3/10. If it’s 3/20 we will get a whole number and if it’s 3/10 we will get a decimal number)

    Step-by-step explanation:

    consider the two parts to be x&y

    x+y = 27 ———–(equation 1)

    1/x + 1/y = 3/10

    (y+x)/xy = 3/10

    [:- since (y+x) = 27]

    27/xy = 3/10

    [cancelling common factors from LHS and RHS]

    9/xy = 1/10

    [ Cross multiplying ]

    90 = xy

    x = 90/y. [ You can also take y = 90/x]

    [ putting the value of x in equation 1 ]

    90/y + y = 27

    90 + y^2 = 27y

    y^2 – 27y + 90 = 0 ( quadratic equation)

    [ y = [(-b) +- √b^2 – 4ac]/2a ]

    [ y = [ -(-27) +- √27^2 – 4×1×90]/2×1 ]

    [ y = [ 27 +- √ 729-360] / 2]

    [ y = [ 27 +- √ 369] / 2 ]

    [ y = [ 27 +- 19.21]/2 ]

    [ y = ( 27 + 19.21 )/2 ] or [ y = ( 27 – 19.21 )/2 ]

    [ y = 23.105 or 3.895]

    [ which is approximately 23 and 4]

    If y = 23

    x + y = 27

    x + 23 = 27

    x = 27 – 23

    x = 4

    Likewise if y = 4, x = 23

    therefore the two parts are 23 & 4( approximately)

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