Question

NEW QUESTION!!!!! VERIFY THAT x3+y3+z3- 3xyx=1/2(x+y+z)[(x-y)2+(y-z)2+(z-x)2]
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HELP ME ⭕⭕⭕⭕
URJENTLY NEEDED.

Answer 1

HoPe mY anSwEr wILL heLp yOu (^o^)

Answer 2

RHS:

Given Equation is (1/2)(x + y + z)[(x - y)^2 + (y - z)^2 + (z - x)^2]

⇒ (1/2)(x + y + z)[x^2 + y^2 - 2xy + y^2 + z^2 - 2yz + z^2 + x^2 - 2zx]

⇒ (1/2)(x + y + z)[2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2zx]

⇒ (1/2)(x + y + z) * 2[x^2 + y^2 + z^2 - xy - yz - zx]

⇒ (x + y + z)[x^2 + y^2 + z^2 - xy - yz - zx]

We know that (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) = a^3 + b^3 + c^3 - 3abc

⇒ x^3 + y^3 + z^3 - 3xyz.

Hope it helps!