Question

Va rog sa ma ajutați cu c.
Legea de compozitie este x*y= xy-k(x+y)+k^2+k, oricare ar fi x, y apartine M, M=[k,+infinit), keR​

Answer 1

$x*y=xy-k(x+y)+k^2+k, \forall x,y\in M,k\in \mathbb{R}<=>x*y=xy-kx-ky+k(k+1), \forall x,y\in M,k\in \mathbb{R}<=>x*y=x(y-k)-k(y-k)+k, \forall x,y\in M,k\in \mathbb{R}<=>x*y=(x-k)(y-k)+k, \forall x,y\in M,k\in \mathbb{R}\\x\in M=>x\ge k=>x-k \ge0 (1)\\y\in M=>y\ge k=>y-k\ge 0(2)\\(1) si (2)=>(x-k)(y-k)\ge 0|+k=>(x-k)(y-k)+k\ge k,\forall x,y\in M,k\in \mathbb{R}=>x*y\ge M, \forall x,y\in M,k\in \mathbb{R}=>x*y\in M,\forall x,y\in M,k\in \mathbb{R}$