Question

3 la puterea n + 3 la puterea n-1 =6 la puterea 2
Aflați n

Answer 1

${3}^{n} + {3}^{n - 1} = {6}^{2}$

${3}^{n - 1} (3 + 1) = 36$

${3}^{n - 1} \times 4 = 9 \times 4$

${3}^{n - 1} \times 4 = {3}^{2} \times 4 \: | \div 4$

${3}^{n - 1} = {3}^{2}$

$n - 1 = 2$

$n = 2 + 1$

$n = 3$

Answer 2

3ⁿ + 3ⁿ⁻¹ = 6²

3ⁿ + 3ⁿ x 3⁻¹ = 36

3ⁿ x ( 1 + 1 / 3 ) = 36

3 ⁿ x ( 3 + 1 )/ 3 = 36

3 ⁿ  x 4 / 3 = 36

3 ⁿ  = 36 : 4 / 3 = 36 x 3 / 4 = 27

3 ⁿ  = 3³ ⇒  n = 3