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

Answer 1

Answer:

567

Step-by-step explanation: hhjj58855787666666777777889999

Answer 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