Question

Va rog raspuns$\sqrt{1+6+6*7^1+6*7^2+...+6*7^{2021}} =49^x$

Answer 1

Răspuns:

1+6+6·7¹+6·7²+...+6·7²⁰²¹ = 7¹+6·7¹+6·7²+...+6·7²⁰²¹ = 7¹(1+6)+6·7²+...+6·7²⁰²¹ = 7¹·7+6·7²+...+6·7²⁰²¹ = 7²+6·7²+...+6·7²⁰²¹ = 7²(1+6)+...+6·7²⁰²¹ =....= 7²⁰²¹·(1+6) = 7²⁰²¹·7 = 7²⁰²²

√(1+6+6·7¹+6·7²+...+6·7²⁰²¹) = 49ˣ

√(7²⁰²²) = (7²)ˣ

7¹⁰¹¹ = 7²ˣ

1011 = 2x

x = 1011/2