Question

Ajutatima va rog.
Redzolvati in R ecuatia:
a)9 la puterea x +8imultit cu 3la puterea x -9=0

Answer 1

$\it 9^x+8\cdot3^x-9=0 \Longrightarrow (3^x)^2+8\cdot3^x-9=0\ \ \ \ (*)\\ \\ \\ Notez\ t=3^x,\ t>0,\ iar\ ecua\c{\it t}ia\ (*)\ devine:\\ \\ \\ t^2+8t-9=0 \Rightarrow t^2+9t-t-9=0 \Rightarrow t(t+9)-(t+9)=0 \Rightarrow \\ \\ \\ \Rightarrow (t+9)(t-1)=0 \Rightarrow \begin{cases}\it t+9=0 \Rightarrow t=-9\ (nu\ convine)\\ \\ \it t-1=0\Rightarrow t=1 \Rightarrow 3^x=1 \Rightarrow x=0 \end{cases}$