Question

Daca x − 1, x + 1 ¸si 2x + 5 sunt termeni consecutivi ai unei progresii
geometrice, atunci valorile lui x sunt:


Multumesc!

Answer 1

Răspuns:

x=-8

Explicație pas cu pas:

daca a1=x-1

a2=a1+r => x-1+r= x+1 => r=2

a3= a1 +2r => x-1+2r = 2x+5 => x=-8

Answer 2

$\it \dfrac{..}{..}\ \ \ \ \ x-1,\ \ x+1,\ \ 2x+5 \Rightarrow (x+1)^2=(x-1)(2x+5) \Rightarrow\\ \\ \Rightarrow x^2+2x+1=2x^2+5x-2x-5 \Rightarrow x^2+x-6=0 \Rightarrow x^2+3x-2x-6=0 \Rightarrow \\ \\ \Rightarrow x(x+3)-2(x+3)=0 \Rightarrow (x+3)(x-2)=0 \Rightarrow x_1=-3,\ \ \ \ x_2=2$