Question

Rezolvati sistemul  in N x N
 $\left \{ {{b+7a=29} \atop {b*a=4}} \right.$

Answer 1

{b+7a=29
{b=4/a

4/a +7a =29

4/a+7a-29=0   aducem la acelasi numitor cu a

4+7a² -29a²=0

7a²-29a +4=0

a=7
b= -29
c=4
Δ= (-29)² -4*7*4=  841 -112=729

x1;x2= (29 +/- √729)/4*7=  (29 +/- 27)/ 28

x1= (29+27)/28=  56/28=2

x2= (29-27)/28= 2/28= 1/14

7a²-29a+4= (x-2)(x-1/14)= (x-2)(x-1/2)=  (x-2)(2x-1)

(x-2)=0   ∧  2x-1=0
x-2=0           2x=1
x=2                 x= 1/2 ∉ N  =>x=2  ,=>b=2  =>a=4/2=2