Question

9^n+9^n+1=10×3^2072
n=?

Answer 1

Răspuns: $\bf n = 1036$

Explicație pas cu pas:

Salutare!

$\bf 9^{n}+9^{n+1}=10\cdot3^{2072}$

$\bf 9^{n}\cdot(9^{n-n}+9^{n+1-n})=10\cdot3^{2072}$

$\bf 9^{n}\cdot(9^{0}+9^{1})=10\cdot3^{2072}$

$\bf 3^{2n}\cdot(1+9)=10\cdot3^{2072}$

$\bf 3^{2n}\cdot 10=10\cdot3^{2072}\:\:\:\Big|:10$

$\bf 3^{2n}=3^{2072}\implies 2n = 2072$

$\bf 2n = 2072 \:\:\:\Big|:2$

$\boxed{\bf n = 1036}$

==pav38==

Answer 2

Răspuns:

Explicație pas cu pas:

9ⁿ + 9ⁿ⁺¹ = 10 x 3²⁰⁷²

9ⁿ + 9ⁿ x 9¹ = 10 x 3²⁰⁷²

9ⁿ x ( 1 + 9 ) = 10 x 3²⁰⁷²

(3²)ⁿ x 10 = 10 x 3²⁰⁷²  l  : 10

3²ⁿ = 3²⁰⁷²

⇒ 2n = 2072 ⇒ n = 2072 : 2  ⇒   n = 1036