if each of a, b and c is a non zero number and a/b = b/c show that (a + b + c)(a – b + c) = a^2 + b^2 + c^2

Question

if each of a, b and c is a non zero number and a/b = b/c show that (a + b + c)(a – b + c) = a^2 + b^2 + c^2

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Serenity 1 month 2021-09-21T22:37:04+00:00 1 Answer 0 views 0

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    2021-09-21T22:38:33+00:00

    Answer:

    Given,

    a+b+c=0

    or, a+b=−c

    cubing both sides we get,

    (a+b)

    3

    =−c

    3

    a

    3

    +b

    3

    +3ab(a+b)=−c

    3

    [∵(a+b)

    3

    =a

    3

    +3a

    2

    b+3ab

    2

    +b

    3

    ]

    a

    3

    +b

    3

    −3abc=−c

    3

    [Since a+b=−c]

    a

    3

    +b

    3

    +c

    3

    =3abc…….(1).

    Now,

    bc

    a

    2

    +

    ac

    b

    2

    +

    ab

    c

    2

    =

    abc

    a

    3

    +b

    3

    +c

    3

    =

    abc

    3abc

    [Using (1)]

    =3.

    Step-by-step explanation:

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