We have $G=(1,2)$ and $x@y=(3xy-4x-4y+6)/(2xy-3x-3y+5)$ .How you find $uin G$ such that $x@u=x$ ?

Question

948 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-28T19:12:28

$u = 3/2$

Solving $x @ u = x$ we have

$(3 x u - 4 x - 4 u + 6)/(2 x u - 3 x - 3 u + 5) = x$

or

$3 x u - 4 x - 4 u + 6 - x (2 x u - 3 x - 3 u + 5)=0$

or

$6 - 4 u - 9 x + 6 u x + 3 x^2 - 2 u x^2=0$

or

$(6-4u)+(6u-9)x+(3-2u)x^2=0$

this relationship must be true for all $x$ so

${(6-4u=0),(6u-9=0),(3-2u=0):}$

and solving for $u$ we have

$u = 3/2$

We have G=(1,2)G=(1,2) and x@y=(3xy-4x-4y+6)/(2xy-3x-3y+5)x@y=(3xy-4x-4y+6)/(2xy-3x-3y+5) .How you find uin Guin G such that x@u=xx@u=x?