On the set of positive rationals,a binary ope | vedclass

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(B) Given the binary operation $a * b = \frac{2ab}{5}$.First,find the identity element $e$ such that $a * e = a$:$\frac{2ae}{5} = a \implies e = \frac

Vedclass · Accepted Answer

$\frac{125}{48}$

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(B) Given the binary operation $a * b = \frac{2ab}{5}$.First,find the identity element $e$ such that $a * e = a$:$\frac{2ae}{5} = a \implies e = \frac{5}{2}$.Next,find the inverse $a^{-1}$ such that $a * a^{-1} = e$:$\frac{2a(a^{-1})}{5} = \frac{5}{2} \implies a^{-1} = \frac{25}{4a}$.For $a = 3$,the inverse is $3^{-1} = \frac{25}{4(3)} = \frac{25}{12}$.Now,solve $2 * x = 3^{-1}$:$\frac{2(2x)}{5} = \frac{25}{12} \implies \frac{4x}{5} = \frac{25}{12}$.$x = \frac{25 	imes 5}{12 	imes 4} = \frac{125}{48}$.

On the set of positive rationals,a binary operation $$ is defined by $a b = \frac{2ab}{5}$. If $2 * x = 3^{-1}$,then $x = $

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On the set of positive rationals,a binary operation $*$ is defined by $a * b = \frac{2ab}{5}$. If $2 * x = 3^{-1}$,then $x = $