If xy-yx- then x-y xy is equal to-

The correct option is D x^xy 1 Given : x^y=y^x ⇒ x = y^xy ( x/y )^xy=x^xyy^xy=x^xyx=x^xy 1 ...

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Dividing a Monomial by a Monomial

If xy=yx, t...

Question

If $x^{y} = y^{x}$ , then ${(\frac{x}{y})}^{\frac{x}{y}}$ is equal to:

x^{\frac{x}{y}}

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x^{\frac{x}{y} - 1}

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x^{\frac{y}{x}}

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x^{\frac{y}{x} - 1}

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Solution

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lim x \to y \frac{X^{Y} - Y^{X}}{X^{X} - Y^{Y}}

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(x / y)^{x / y}

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{(\frac{x}{y})}^{x / y} =

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= π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

{t a n}^{- 1} \sqrt{{\frac{x (x + y + z)}{y z}}} + {t a n}^{- 1} \sqrt{{\frac{y (x + y + z)}{z x}}} + {t a n}^{- 1} \sqrt{{\frac{z (x + y + z)}{x y}}} =

(1 - x^{2}) (1 - y^{2}) + 4 x y

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