Question

8.aflati numerele naturale x si y,stiind ca:a)(2*x+3)*(2*x+4)=56b)(2*x+1)*(2*x+2)*(2*x+3)=720c)(x-1)*(y+2)=13

Answer 1

a) x=2
b)nu are solutii naturale
c)x=2, y=11

Answer 2

1)(2*x+3)*(2*x+4)=56 =7*8
Se observa ca numerele (2*x+3) si (2*x+4) sunt consecutive=>
2x+3=7
2x=7-3
2x=4
x=4:2
x=2
2)(2*x+1)*(2*x+2)*(2*x+3)=720=8*9*10

Se observa ca numerele (2*x+1), (2*x+1) si (2*x+3) sunt consecutive=>
2x+1=8
2x=7
x=7/2
Ecuatia nu are radacini naturale.
3)(x-1)*(y+2)=13=1*13=13*1
x-1=1=>x=2
y+2=13=>y=11

x-1=13=>x=14
y+2=1=>y=-1(nu este numar natural)
Solutia ecuatiei este perechea (2;11).