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Question

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


A
xyz=1
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B
xyz=1
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C
x+y+z=1
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D
xz=y
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Solution

The correct option is A $$xyz = 1$$
$$\displaystyle z=x^{y}=(y^{z})^{y}$$                               ...$$\displaystyle (\because x=y^{z})$$
             $$\displaystyle =y^{zy}=(z^{x})^{zy}=z^{xyz}$$      ...$$\displaystyle (\because y=z^{x})$$
$$\displaystyle \therefore z^{1}=z^{xyz}$$
$$\Rightarrow xyz=1$$

Mathematics

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