Question

$G$ is a set of all rational numbers except $-1$ and $\ast$ is defined by $a\ast b=a+b+ab$ for all $a,b\in G$, in the group $(G,\ast )$, the solution of $2^{-1}\ast x\ast 3^{-1}=5$ is

• A. $71$
• B. $68$
• C. $63/5$
• D. $72/5$

Answer 1

The correct option is A $71$

The solution for $2^{-1}\ast x\ast 3^{-1}=5$ is
$\Rightarrow x=2\ast (5\ast 3)=2\ast (5+3+15)$
$=2\ast \left(23\right)=2+23+46=71$