Question

Aflati numarul x, stiind ca 7^x+7^2x+7^x+3=19257

Answer 1

19257=$7^{2}$[1+$7^{2}$(1+7)]=$7^{2}$*(1+$7^{2}$+$7^{3}$)

$7^{x}$+$7^{2x}$+$7^{x+3}$=$7^{x}$+$7^{2x}$+$7^{x} * 7^{3}$)=$7^{x}$*(1+$7^{x}$+$7^{3}$)

Din cele doua relatii de mai sus observam ca x=2.

Answer 2

19257=$7^{2}$ * [1+ $7^{2}$ * (1+7)]=$7^{2}$ * (1+$7^{2}$ + $7^{3}$)

$7^{x}$ + $7^{2x}$ + $7^{x+3}$ = $7^{x}$ + $7^{2x}$ + $7^{x} * 7^{3}$ = $7^{x}$ * (1+ $7^{x}$ + $7^{3}$)

Din cele doua relatii de mai sus observam ca x=2.