If x = a^2-bc, y = b^2-ac, z=c^2-ab
Then prove that x^3+y^3+z^3-3xyz is a perfect square

Question

If x = a^2-bc, y = b^2-ac, z=c^2-ab
Then prove that x^3+y^3+z^3-3xyz is a perfect square

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Samantha 2 years 2021-07-08T05:00:12+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-08T05:01:13+00:00

    Answer:

    567

    Step-by-step explanation: hhjj58855787666666777777889999

    0
    2021-07-08T05:02:10+00:00

    Answer:

    Prove that:-

    (x/a)^3+(y/b)^3+(z/c)^3 = 3x.y.z/a.b.c.

    L.H.S.

    =(x/a)^3+(y/b)^3+(z/c)^3.

    We have on adding eq.(1) ,(2) & (3).

    x/a+y/b+z/c=b-c+c-a+a-b =0.

    If x/a+y/b+z/c=0 then

    (x/a)^3+(y/b)^3+(z/c)^3=3×(x/a)×(y/b)×(z/c).

    or (x/a)^3+(y/b)^3+(z/c)^3 =3.x.y.z/a.b..c.

    Proved.

    Hope it helps

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