Question

verify x^3+y^3+z^3=3xyz​

Answer 1

First we take R.H.S and use the formula [(a - b)²=a²+b²-2ab] and simplify it then R.H.S will be equal to LHS

R.H.S

=1/2×(x+y+z) (x²+y²-2xy+y²+z²-2yz+x²+z²-3xz)

=1/2×(x+y+z) (2x²+2y²+2z²-2xy-2yz-2xz)

=1//2×(x+y+z) 2(x²+y²+z²-xy-yz-xz)

=(x+y+z) (x²+y²+z²-xy -yz -xz)

=x³+y³+z³-3xyz

L.H.S

we know that,

[x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-xz)

L.H.S=R.H.S

[x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-xz)

Hope it helps you.

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