solve the following a(x+y)+b(x-y)-(a²-ab+b²)=0 and a(x+y)-b(x-y)-(a²+ab+b²)=0​

Question

solve the following a(x+y)+b(x-y)-(a²-ab+b²)=0 and a(x+y)-b(x-y)-(a²+ab+b²)=0​

in progress 0
Nevaeh 1 month 2021-08-06T08:01:58+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-06T08:03:56+00:00

    Step-by-step explanation:

    Taking x+y=u and x−y=v the given system of equations becomes

    au+bu−(a

    2

    −ab+b

    2

    )=0

    au−bv−(a

    2

    +ab+b

    2

    )=0

    By cross-multiplication, we have

    b×−(a

    2

    +ab+b

    2

    )−(−b)×−(a

    2

    −ab+b

    2

    )

    u

    =

    a×−(a

    2

    +ab+b

    2

    )+a(a

    2

    −ab+b

    2

    )

    −v

    =

    a×−b−a×b

    1

    −b(a

    2

    +ab+b

    2

    )−−b(a

    2

    −ab+b

    2

    )

    u

    =

    −a(a

    2

    +ab+b

    2

    )+a(a

    2

    −ab+b

    2

    )

    −v

    =

    −ab−ab

    1

    −b(a

    2

    +ab+b

    2

    +a

    2

    −ab+b

    2

    )

    u

    =

    −a(a

    2

    +ab+b

    2

    −a

    2

    +ab−b

    2

    )

    −v

    =

    −2ab

    1

    −2b(a

    2

    +b

    2

    )

    u

    =

    −a(2ab)

    −v

    =

    −2ab

    1

    ⇒u=

    −2ab

    −2b(a

    2

    +b

    2

    )

    ,v=

    −2ab

    2a

    2

    b

    ⇒u=

    a

    a

    2

    +b

    2

    ,v=−a

    Now, u=

    a

    a

    2

    +b

    2

    ⇒x+y=

    a

    a

    2

    +b

    2

    .(i)

    and, v=−a⇒x−y=−a ..(ii)

    Adding equations (i) and (ii), we get

    2x=

    a

    a

    2

    +b

    2

    −a⇒2x=

    a

    a

    2

    +b

    2

    −a

    2

    ⇒2x=

    a

    b

    2

    ⇒x=

    2a

    b

    2

    Substitutiing equation (ii) from equation (i), we get

    2y=

    a

    a

    2

    +b

    2

    +a⇒2y=

    a

    a

    2

    +b

    2

    +a

    2

    ⇒y=

    2a

    2a

    2

    +b

    2

    Hence, the solution of the given system of equations is x=

    2a

    b

    2

    ,y=

    2a

    2a

    2

    +b

    2

    .

Leave an answer

Browse

9:3-3+1x3-4:2 = ? ( )