Question

Sa se afle numerele naturale x si y stiind ca: a) (x+6)(y+5)=72 ; b) (x+3)(y+4)=30 ; c) (2x+1)(y-2)=36 ; d) (3x+3)(2y-4)=48. [IN MAXIM 5-10MIN]

Answer 1

a)(x+6)x(y+5)=72
72=8x9
x+6=8
x=8-6=2
x=2

y+5=9
x=9-5
x=4

b)(x+3)x(y+4)=30
30=6x5
x+3=6
x=6-3
x=3
y+4=5
x=5-4
x=1

c)(2x+1)x(y-2)=36
36=9x4
2x+1=9
2x=9-1
2x=8
x=8:2
x=4

y-2=4
x=4+2
x=6

d)(3x+3)x(2y-4)=48
48=6x8
3x+3=6
3x=6-3
3x=3
x=3:3
x=1
2y-4=8
2y=8+4
2y=12
y=12:2
y=6

Answer 2

a) (x+6)(y+5)=72
Descompunem 72 in 8•9
x+6=8
y+5=9
x=2; y=4

x+6=9
y+5=8
x=3; y=3

b) (x+3)(y+4)=30
Descompunem 30 in 3•10
x+3=3
y+4=10
x=0; y=6
Descompunem 30 in 5•6
x+3=5
y+4=6
x=2, y=2;

x+3=6
y+4=5
x=3, y=1

c) (2x+1)(y-2)=36
Descompunem 36 in 9•4
2x+1=9
y-2=4
x=4; y=6

d) (3x+3)(2y-4)=48
Descompunem 48 in 6•8
3x+3=6 x=1
2y-4=8. y=6