Question

cum se rezolva sistemul axb=420; (a+5)(b-2)=420?

Answer 1

Explicație pas cu pas:

(a+5)(b-2)=420 =>

ab+5b-2a-10=420 =>

420+5b-2a-10=420 =>

5b-2a-10=0 =>

5b-2a=10 => 2a=5b-10

a*b=420 => 2*a*b=840 =>(5b-10)b=840 =>

5b²-10b-840 =0 =>

5(b²-2b-168)=0 =>

b²-2b-168 =0 =>

b²-14b+12b-168=0 =>

b(b-14)+12(b-14)=0 =>

(b-14)(b+12)=0 <=>

b-14=0 =>b=14

sau

b+12=0 =>b=-12

=> 2a=5*14-10 => 2a=70-10 => a=30

sau

2a=5*(-12)-10 => 2a=-60-10 => 2a=-70 =>

a=-35

(a,b)€{(30,14);(-35,-12)}