Question

Determinati xeR stiind ca numerele 2,4 si x+5 sunt termeni consecutivi ai unei progresii geometrice.

Answer 1

2.4.x+5
Pg⇒b=√a×c
a=2
b=4
c=x+5
4=√2(x+5)⇒
ca sa putem elimina radicalul ridicam la puterea a 2 si  avem
(4)²=(√2(x+5)²⇒16=2(x+5)⇒16=2x+10⇒2x=16-10⇒2x=6⇒x=6/2
⇒x=3
sucees

Answer 2

2;4;x+5- progresie geometrica
Aplicam aceasta formula:
[tex]b^{2}=ac =\ \textgreater \ 4^{2}=2(x+5)\ \textless \ =\ \textgreater \ 16=2x+10=\ \textgreater \ 2x=6 |:2 =\ \textgreater \ x=3~ [/tex]
$~Deci~x~este~egal~cu~3.$
2; 4;3+5
2; 4 8 (True)