Question

14. Găseste numerele naturale necunoscute. (4 + a) x (6-b) = 12 (16-a) x (b + 3) = 15 (3 + a) x (b-5) = 18 X​

Answer 1

Răspuns:

a) (4+a) x(6-b)=12     caz 1. (4+a)x(6-b)= 4x3=>

4+a= 4    => a= 4-4 =0    a=0

6- b= 3     => b= 6-3= 3   b=3

caz 2.  (4+a)x(6-b)= 6x2=>

4+a=6 => a= 6-4=2   a=2

6-b= 2=> b= 6-2=4   b=4

caz 3.  (4+a)x(6-b)= 12x1 =>

4+a= 12 => a= 12- 4=8    a=8

6-b=1 => b= 6-1= 5    b= 5

b) (16-a) x (b + 3) = 15      caz1. (16-a) x (b + 3)=5 x3 =>

16- a= 5 => a= 16-5= 11   a= 11

b+3=3 => b= 3-3=0    b=0

caz 2.  (16-a) x (b + 3)= 3x5  =>

16-a=3    => a= 16-3=13   a=13

b+3=5   =>   b= 5-3=2    b=2

caz 3.  (16-a) x (b + 3)=1x15

16-a= 1 => a= 16-1=15   a=15

b+3= 15 => b= 15-3=12   b=12

c) (3 + a) x (b-5) = 18     caz 1. (3 + a) x (b-5) = 6x3

3+a=6=>  a= 6-3=3   a=3

b-5= 3  => b=3+5=8    b=8

caz2. (3 + a) x (b-5) = 9x2

3+a=9 => a= 9-3=6     a=6

b-5=2 =>  b=2+5= 7    b=7

caz3. (3 + a) x (b-5) = 18x1

3+a=18 => a=18- 3=15    a=15

b-5=1  =>b=1 +5= 6     b=6