if xy=6 and x²+y²=5 then the value of (x+y)² is​

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if xy=6 and x²+y²=5 then the value of (x+y)² is​

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Samantha 4 weeks 2021-08-14T08:23:53+00:00 1 Answer 0 views 0

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    2021-08-14T08:25:07+00:00

    Answer:

    We are given that

    xy = 2 ……………….(1)

    and x^2 + y^2 = 5 …………………..(2)

    Since we know that

    (x+y)^2 = x^2 + y^2 + 2xy

    From (1) and (2) substituting the values, we get

    (x+y)^2 = 5 + 2*2

    (x+y)^2 = 9

    therefore x+y = 3 or -3

    Taking x+y = 3 …………….(3)

    Solving (1) and (3)

    we get the quadratic equation

    x^2 – 3x +2 = 0

    Solving it we get x = 2 ,1

    putting in (1)

    we get y = 1, 2 respectively

    Therefore x=1 and y=2 or x=2 and y=1

    Now considering x + y = -3 …………..(4)

    Solving (1) and(4) we get the quadratic equation as

    x^2 + 3x +2 = 0

    Solving it we get

    x = -2,-1

    putting these values of x in (1) we get

    y = -1, -2 respectively.

    Therefore x=-1, y= -2 or x= -2, y=-1

    Hence we get overall 4 solutions for x and y.

    x=1, y= 2.

    x= 2, y= 1.

    x = -1, y= -2.

    x= -2, y= -1.

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