Question

2 la puterea x +2•2 la puterea -x =3

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$\it 2^x+2\cdot2^{-x}=3 \Rightarrow 2^x+2\cdot\dfrac{1}{2^x}=3\ \ \ \ \ (*)\\ \\ \\ Not\breve am\ 2^x=t,\ t > 0,\ iar\ ecua\c{\it t}ia\ devine:\\ \\ t+2\cdot\dfrac{1}{t}-3=0\Big|_{\cdot t} \Rightarrow t^2+2-3t=0 \Rightarrow t^2-t-2t+2=0 \Rightarrow \\ \\ \Rightarrow t(t-1)-2(t-1)=0 \Rightarrow (t-1)(t-2)=0 \Rightarrow t_1=1;\ \ t_2=2.\\ \\ Revenim\ asupra\ nota\c{\it t}iei:\\ \\ t_1=1 \Rightarrow 2^x=1 \Rightarrow x_1=0\\ \\ t_2=2 \Rightarrow 2^x=2 \Rightarrow x_2=1$