If √(x/y) = 10/3 – √(y/X) and x – y = 8, then the value of xy is equal to :

(a) 36
(b) 24
(c) 16
(d) 9

Anurag Mishra Professor Asked on 20th February 2016 in Maths.
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  • 1 Answer(s)

    Answer: (d) 9

    Solution:-
    √(x/y) = 10/3 – √(y/x)
    √(x/y) + √(y/x)  = 10/3
    (x + y)/√xy = 10/3
    Square on both side,
    (x + y)²/xy = 100/9
    (x² + y² + 2 xy)/xy = 100/9
    By cross multiplication,
    9 (x² + y²) + 18 xy  = 100 xy
    9 (x² + y²) = 100 xy – 18 xy
    9 (x² + y²) = 82 xy         …………………….. (1)

    x – y = 8
    Square on both side,
    (x – y)² = 64
    x² + y² – 2 xy = 64
    x² + y² = 64 + 2 xy

    Put the value of x² + y² = 64 + 2 xy in equation (1),
    Then, 9 (64 + 2 xy) = 82 xy
    9 x 64 + 18 xy = 82 xy
    9 x 64 = 82 xy – 18 xy
    9 x 64 = 64 xy
    xy = 9 x 64/64
    xy = 9

    Then, the value of xy is 9.

    Hence, the correct answer is option (d) 9.

    Anurag Mishra Professor Answered on 20th February 2016.
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