Question

Determinati valorile nat ale nr n si cifra x pentru care are loc egalitatea:
3^(n+6)+3^(n+5)+3^(n+4)+2·3^(n+3)+4·3^n=xxxx (cu bara de asupra)
Parantezele nu fac parte din exercitiiu le-am pus ca sa nu va incurce”!Multumesc!

Answer 1

$3^{n+6}+3^{n+5}+3^{n+4}+2*3^{n+3}+4*3^n=\overline{xxxx}$
$3^n*3^6+3^n*3^5+3^n*3^4+2*3^n*3^3+4*3^n=\overline{xxxx}$
$3^n(3^6+3^5+3^4+2*3^3+4)=\overline{xxxx}$
$3^n(729+243+81+54+4)=\overline{xxxx}$
$3^n*1111=\overline{xxxx}$
=> n=0=> x= 1
n=1=>x=3
n=2=>x=9