Question

Se da legea x*y=xy-x-y+5

1)x*x=8
2)Determinati numarul perechilor de numere intregi (m,n) stiind ca m*n=5

Answer 1

"Se observa" ca legea poate fi scrisa
x*y=xy-x-y+1+4
sau
x*y= (x-1)(y-1)+4
x*x=(x-1)²+4=8
(x-1)²=4
x-1=2....x=3
x-1=-2....x=-1
x∈{-1;3}


m*n=(m-1)(n-1)+4=5
(m-1)(n-1)=1=1*1=(-1)(-1)

m-1=1.... m=2
n-1=1....n=2


m-1=-1  m=0
n-1=-1...n=0
(m;n)∈{(2;2);(0;0)} 2 perechi de numere intregi