what should be added to y^2,+4xy to make it a perfect sq​

Question

what should be added to y^2,+4xy to make it a perfect sq​

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Vivian 16 mins 2021-10-13T02:16:59+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-13T02:18:28+00:00

    Answer:

    By adding four we can make it perfect square

    4

    x

    2

    +

    8

    x

    +

    4

    (

    2

    x

    )

    2

    +

    2

    2

    x

    2

    +

    (

    2

    )

    2

    (

    2

    x

    +

    2

    )

    2

    Thus it becomes a perfect square

    But how do we get to this answer without any guess , here’s the role of discriminant.

    Any quadratic equation is of form

    a

    x

    2

    +

    b

    x

    +

    c

    =

    0

    Here , discriminant

    (

    d

    )

    =

    b

    2

    4

    a

    c

    For perfect squares it is

    0

    So , we get

    0

    =

    8

    2

    4

    ×

    4

    ×

    c

    64

    =

    16

    c

    c

    =

    4

    That’s the answer

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