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Higher Order Derivatives

23. Xyz plus ...

Question

23. Xyz plus xy + Y Z plus ZX plus X + Y + Z equal to 289 find the value of x + Y + Z

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x + y + z = 1

x y + y z + z x = - 1

x y z = - 1

, find the value of

x^{3} + y^{3} + z^{3}

.

x + y + z = x y z

\frac{x + y}{1 - x y} + \frac{y + z}{1 - y z} + \frac{z + x}{1 - z x} = \frac{x + y}{1 - x y} \cdot \frac{y + z}{1 - y z} \cdot \frac{z + x}{1 - z x}

x + y + z = 1, x y + y z + z x = - 1

x y z = - 1

x^{3} + y^{3} + z^{3}

x, y

z

x y + x + x + y = 23, y z + y + z = 31, z x + z + x = 4

x^{y} = z, y^{z} = x

z^{x} = y

, then Find xyz

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