Question

if x=(-1/3)^-3÷(2/3)^-4,find the value of (x/y+y/x)^-1​

Answer 1

Answer:

The value of expression $[\frac{x}{y} + \frac{y}{x}]^{-1}$  is $\dfrac{73}{36}$  .

Step-by-step explanation:

Given as :

$\dfrac{x}{y}$   = $\dfrac{(\frac{-1}{3})^{-3}}{(\frac{2}{3})^{-4}}$

Or, $\dfrac{x}{y}$ = $\dfrac{-27}{\frac{81}{8}}$

Or, $\dfrac{x}{y}$ = $\dfrac{-24}{9}$                  ......A

So The value of given expression  $[\frac{x}{y} + \frac{y}{x}]^{-1}$

Or, $[\frac{x^{2}+y^{2}}{xy} ]^{-1}$

or, $[\dfrac{xy}{x^{2}+y^{2}} ]^{1}$

Or, $\dfrac{y}{x}$ + $\dfrac{x}{y}$

Or,  $\dfrac{-9}{24}$ - $\dfrac{24}{9}$

Or, $\dfrac{-81-576}{216}$

Or, $\dfrac{657}{216}$

Or, $\dfrac{73}{36}$

Hence, The value of expression $[\frac{x}{y} + \frac{y}{x}]^{-1}$  is $\dfrac{73}{36}$  . Answer