Question

nr. nat. x care verifica egalitatea
$\sqrt{1 \times 6 + 5 \times 6 + 5 \times {6}^{2} + 5 \times 6 {}^{3} + .... + 5 \times {6}^{2019} } = {36}^{101x}$
a. x=3
b. x=4
c. x=5
d. x=6​

Answer 1

Răspuns:

Explicație pas cu pas:

Suma de sub radical:

1*6 +5*6(1 +6 +6^2 +6^2 +...+6^2018) =

6 +5*6( 6^2019  -1)/(6-1) =

6 + 6( 6^2019  -1) = 6 +6^2020 -6 = 6^2020

√6^2020  = 6^1010

6^1010 = 36^(101*x) = 6^202x

1010 =202*x

x = 1010:202 = 5