Question

Cele 2 exercitii va rog mult ​

Answer 1

Răspuns:

Explicație pas cu pas:

a= √(x+2)²+√(x-5)²=|x+2|+|x-5|

pt x=-2, a=0+|-7|=0+7=7∈N

ptx=5, a=|7|+0=7 ∈N

pt x∈(-2;5), x+2>0 si x-5<0

deci |x+2|=x+2

si

|x-5|= -(x-5) =-x+5

atunci a=x+2+(-x+5)=7∈N

exe 2

(x+2)/(x-1)∈N

(x-1+3)/(x-1)∈N

1+3/(x-1)∈N

dar 1∈N

deci 3/(x-1)∈N

x-1∈D3N={1;3}

x∈{2;4}=A

-2≤4x-6<10 |+6

4≤4x<16 |:4

1≤x<4⇔x∈[1;4) pt ca x∈R

B=[1;4)

{1;3}∩[1;4)={1;3} adica A∩B=A