Question

Va rog ajutorrr...!!!!!!!!

Answer 1

$-1<x,y<-1\\ \\ xy\in~(1,1)~\\ \\ -1<\frac{x+y}{1+xy} <1~|*(1+xy)\\ \\ -1-xy<x+y<1+xy\\ \\ 1)-1-xy<x+y\\ \\ x+y+xy>-1\\ \\ Deoarece~x,y\in~(-1,1),~inseamna~ca~x+y\in~(-2,2)~si~daca~aduni~xy~\in~(1,1)~vei~avea~ca:\\ x+y+xy>-1~~ (@)\\ \\ 2) x+y<1+xy\\ \\ x+y-xy<1\\ \\ Iar,~daca~x+y\in(-2,2)~si~xy\in~(1,1),~inseamna~ca:\\ \\ x+y-xy\in~(-2-1,2-1)=(-3,1)<1~(@@)\\ \\ Din~(@)~si~(@@)~iti~rezulta~concluzia!$