Question

x,y ∈ IN fractia
¹²⁻x(2y+1)+2y+1     sa fie
A)echiunitara
B)echivalenta cu ⁻⁴₃

Answer 1

Adica, asa ?
$\frac{12}{x(2y+1)+2y+1}=1 \\ x(2y+1)+2y+1}=12 \\ 2xy+x+2y=11 \\ x=1;2y+1+2y=11;4y=10;2y=5 \\ x=2;4y+2+2y=11;6y=9 \\ x=3;6y+3+2y=11;8y=8;y=1$
deci, $x=3;y=1$
$\frac{12}{x(2y+1)+2y+1}= \frac{4}{3} \\ 4[x(2y+1)+2y+1]=36 \\ x(2y+1)+2y+1=9 \\ x(2y+1)+2y=8 \\ x=1;2y+1+2y=8;4y=7 \\ x=2;4y+2+2y=8;6y=6;y=1$
deci, $x=2;y=1$