Question

daca a+1/2 = 10/a unde a este un numar natural atunci valoarea lui a este egala cu:?

Answer 1

Răspuns: $\Large \boxed{\Large\bf a =4 \in \mathbb{N}}$

Explicație pas cu pas:

Buna!

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$\large\bf \dfrac{a+1}{2}=\dfrac{10}{a}\implies a\cdot(a+1)= 2\cdot 10\implies$

$\large\bf a^{2} +a= 20\implies a^{2} +a- 20=0\implies$

$\large\bf a^{2} +5a-4a-20=0\implies a\cdot(a+5)-4\cdot(a+5)=0\implies$

$\large\bf (a+5)\cdot(a-4)=0\implies$

$\large\bf a+5=0\implies a = -5 \not\in \mathbb{N}$

$\large\bf a-4=0\implies \boxed{\large\bf a =4 \in \mathbb{N}}$

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