Question

On the set of positive rational a binary operation is defined by a star b is equals to 2 a b divided by 5 if two star x is equal to 3 raise to minus 1 then x is equal to

Answer 1

$\textbf{Given:}$

$a*b=\dfrac{2\,ab}{5}\;\text{and}\;2*x=3^{-1}$

$\textbf{To find:}$

$\text{The value of x}$

$\textbf{Solution:}$

$\text{Consider,}$

$2*x=3^{-1}$

$\implies\,\dfrac{2\,(2x)}{5}=3^{-1}$

$\implies\,\dfrac{4x}{5}=\dfrac{1}{3}$

$\implies\,x=\dfrac{5}{3{\times}4}$

$\implies\bf\,x=\dfrac{5}{12}$

$\textbf{Answer:}$

$\textbf{The value of x is \bf\dfrac{5}{12} }$

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