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Multiple Choice Questions

what is relationship between x and y ........

Quantitative Aptitude (CDS) Algebra

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$If \: x=t^{\frac{1}{t-1}}\: and\: y\: =\: t^{\frac{t}{t-1}}, t>0,t\neq 1,then$

what is relationship between x and y?

$y^{x}=x^{\frac{1}{y}}$

$x^{\frac{1}{y}}=y^{\frac{1}{x}}$

$x^{y}=y^{x}$

$x^{y}=y^{\frac{1}{x}}$

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Explanation:

As, $x=t^{\frac{1}{t-1}} , y =\: t^{\frac{t}{t-1}}$
$y=(t^{t})^{\frac{1}{t-1}}$
$=> y=t^{\frac{t}{t-1}}$
$=> y=t^x$
$=> t=(y)^{\frac{1}{x}}-----------(i)$
$x=t^{\frac{t}{t-1}}$
$x^{t}=t^{\frac{t}{t-1}}-------------(ii)$
From (i) and (ii)
$x^{\frac{y}{x}}=y$
$x^{y}=y^{x}$

By: Munesh Kumari

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