Question

Afla numarul natural A care verifica relatia: {[(2a-3) x 2 - 2 la patrat]: 5 + 103 la puterea 0} x 3 - 1 la 2018 = 8.

Answer 1

$\bf \Big\{ \big[(2a-3 \big)\cdot 2-2^{2}\big]: 5+103^{0}\Big\}\cdot3-1^{2018} = 8$

$\bf \Big\{ \big[\big(2a-3\big)\cdot 2 - 4\big]:5+1 \Big\}\cdot 3-1 = 8$

$\bf \Big[\big(4a-6- 4\big):5+1\Big]\cdot3 = 8+1$

$\bf \Big[ \big(4a-10\big):5+1\Big]\cdot3 = 9~~~\bigg|:3$

$\bf \big(4a-10\big):5+1 = 3$

$\bf \big(4a-10\big):5 = 3-1~~~\bigg|\cdot5$

$\bf 4a-10= 2 \cdot 5$

$\bf 4a= 10+10$

$\bf 4a=20~~~\bigg|:4$

$\large \red{\boxed{\bf a=5}}$

Câteva formule pentru puteri:

a⁰ = 1 sau 1 = a⁰

(- a)ⁿ, unde n este o putere para (-a)ⁿ = aⁿ

aⁿ · aᵇ = (a · a) ⁿ ⁺ ᵇ  sau  (a · a) ⁿ ⁺ ᵇ = aⁿ · aᵇ

aⁿ : aᵇ = (a : a) ⁿ ⁻ ᵇ sau (a : a) ⁿ ⁻ ᵇ = aⁿ : aᵇ

aⁿ · bⁿ = (a · b)ⁿ   sau   (a · b)ⁿ = aⁿ · bⁿ

aⁿ : bⁿ = (a : b)ⁿ sau (a : b)ⁿ = aⁿ : bⁿ

(aⁿ)ᵇ = aⁿ ˣ ᵇ   sau aⁿ ˣ ᵇ = (aⁿ) ᵇ

Bafta multa !