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

2 thoughts on “If x = a^2-bc, y = b^2-ac, z=c^2-ab<br /> Then prove that x^3+y^3+z^3-3xyz is a perfect square <br />”

1. Answer:

   567

   Step-by-step explanation: hhjj58855787666666777777889999

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2. 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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