The sum of square and product of two number are 557 & 266 respectively

The sum of square and product of two number are 557 & 266 respectively. The numbers will be-
(a) 7,6
(b) 27, 23
(c) 17, 14
(d) 19, 14

Anurag Mishra Professor Asked on 8th March 2016 in Maths.
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  • 1 Answer(s)

    Answer: (d) 19, 14

    Solution:-
    Let the two number be X and Y.

    The sum of square and product of two numbers are 557 & 266
    Then, X² + Y² = 557  & X Y = 266

    Now, (X + Y)² = X² + Y² + 2 x X Y
    = 557 + 2 x 266
    (X + Y)² = 1089
    Square root on both side,
    X + Y = 33 ………….. (1)

    (X – Y)² = X² + Y² – 2 x X Y
    = 557 – 532
    (X – Y)² = 25
    Square root on both side,
    X – Y = 5 ……………. (2)

    Add equation (1) & (2),
    X + Y + X – Y = 33 + 5
    2 X = 38
    X = 38/2
    X = 19
    Put the value of X = 19 in equation (1),
    Then, 19 + Y = 33
    Y = 33 – 19
    Y = 14

    Then, two numbers are 19, 14.

    Hence, the correct answer is option (d) 19, 14.

    Anurag Mishra Professor Answered on 8th March 2016.
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