Question

afla numerele naturale a si b care verifica egalitatea : a ( b - 2 )-3 (b -2) = 10
dau coroana !!!


Answer 1

(1) a(b-2)-3(b-2) = 10=>(b-2)(a-3)=10
(2) 10=10*1=1*10=5*2=2*5
Aplicam a*b=c*d=>a=c si b=d (3)
Din (1), (2) si (3)=>(b-2)(a-3)=10
Pentru (b-2)(a-3)=10*1
=>b-2=10=>b=10+2=>b=12
=>a-3=1=>a=1+3=>a=4
Pentru (b-2)(a-3)=1*10=>
=>b-2=1=>b=1+2=>b=3
=>a-3=10=>a=10+3=>a=13
Pentru (b-2)(a-3)=5*2=>
=>b-2=5=>b=5+2=>b=7
=>a-3=2=>a=2+3=>a=5
Pentru (b-2)(a-3)=2*5=>
=>b-2=2=>b=2+2=>b=4
=>a-3=5=>a=5+3=>a=8
Deci (a,b)={(4,12); (13,3); (5,7); (8,4)}