If $x = y^{z}, y = z^{x}$ and $z = x^{y}$ , then

\frac{x y}{z} = 1

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x y z = 1

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x + y + z = 1

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x z = y

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Solution

The correct option is A $x y z = 1$
$z = x^{y} = (y^{z})^{y}$ ... $(∵ x = y^{z})$
$= y^{z y} = (z^{x})^{z y} = z^{x y z}$ ... $(∵ y = z^{x})$
$∴ z^{1} = z^{x y z}$
$\Rightarrow x y z = 1$

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If x+y+z=6, xy+xz+yz=11, xyz=6 thenequals

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