The value of x - y - zx-1y-1 - y-1z-1 - z-1x-1 is-

The correct option is A xyz #160;The given expression is x+y+z x ^ 1 y ^ 1 + y ^ 1 z ^ 1 + z ^ 1 x ^ 1 = x+y+z 1 xy + ...

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Inequalities Involving Mathematical Means

The value of ...

Question

The value of $\frac{x + y + z}{x^{- 1} y^{- 1} + y^{- 1} z^{- 1} + z^{- 1} x^{- 1}}$ is:

\frac{1}{x y z}

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\frac{1}{x y} + \frac{1}{y z} + \frac{1}{x z}

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x y z

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x y + y z + z x

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Solution

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

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 = 1

x y + y z + z x = - 1

x y z = - 1

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

If x+y+z=1,xy+yz+zx=-1 and xyz=-1 , x³+y³+z³=?

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