Question

2. Gasiti numerele naturale x si y, y> 1. astfel incât fractia 2010/(x+5)•(y-1) sa fie echiunitara.

Answer 1

2010/(x+5)*(y-1)= este echiunitara daca numitorul este egal cu numaratorul
2010=(x+5)(y-1)
xy-x+5y-5=2010
xy-x+5y=2010+5
x(y-1)+5y=2015
x(y-1)=2000
5y=15
y=15/5
y=3
x(3-1)=2000
2x=2000
x=1000

Answer 2

2010=2 ×3×5×67
2010/(x+5)(y-1)=1
2010=(x+5)(y-1)
y-1=2 
2010=x+5
x=2005
y=3

y-1=3
2010=(x+5)×3
x+5=670
x=665
y=4

y-1=5
2010=(x+5)×5
x+5=402
x=397
y=6

y-1=67
2010=(x+5)×67
x+5=30
x=25
y=67

x+5=5
2010=5(y-1)
y-1=402
x=0
y=403

x+5=67
2010=67(y-1)
y-1=30
x=62
y=31