Răspuns: [tex]\Large \boxed{\Large\bf a =4 \in \mathbb{N}}[/tex]
Explicație pas cu pas:
Buna!
[tex]\it~~[/tex]
[tex]\large\bf \dfrac{a+1}{2}=\dfrac{10}{a}\implies a\cdot(a+1)= 2\cdot 10\implies[/tex]
[tex]\large\bf a^{2} +a= 20\implies a^{2} +a- 20=0\implies[/tex]
[tex]\large\bf a^{2} +5a-4a-20=0\implies a\cdot(a+5)-4\cdot(a+5)=0\implies[/tex]
[tex]\large\bf (a+5)\cdot(a-4)=0\implies[/tex]
[tex]\large\bf a+5=0\implies a = -5 \not\in \mathbb{N}[/tex]
[tex]\large\bf a-4=0\implies \boxed{\large\bf a =4 \in \mathbb{N}}[/tex]
#copaceibrainly