Question

Here is a question to test your maths!​

Answer 1

hope it helps.........!

Answer 2

AnsweR :-

Let's take RHS and LHS

RHS first :-

$\sf \dfrac{1}{2}(x + y + z)( {x - y}^{2}) + ( {y - z)}^{2} + ( {z - x)}^{2}$

Since ${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

$\sf \dfrac{1}{2}[(x + y + z)( {x}^{2} - {y}^{2} - 2xy) + ( {y}^{2} + {z}^{2} - 2yz) + ( {z}^{2} + {x}^{2} - 2zx)]$

$\sf \dfrac{1}{2}[(x + y + z)( {2x}^{2} + {2y}^{2} + {2z}^{2} - 2xy - 2yz - 2zx)]$

$\sf \dfrac{1}{2}(x + y + z)2( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)$

$\sf(x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zy)$

Now L.H.S :-

we know that

→$\sf {x}^{3} + {y}^{3} + {z}^{3} - 3xyz$

$\sf (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)$

$\sf {x}^{2} + {y}^{2} + {z}^{2} - 3xyz$

$\therefore$ L.H.S = R.H.S

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