Răspuns:
[tex]$\mathbf{x = 0}$[/tex]
Explicație pas cu pas:
[tex]$\mathbf{3 {}^{2x} + 2 \times 3 {}^{x} - 3 = 0 }$[/tex]
[tex]$\mathbf{( {3}^{x} ) {}^{2} + 2 \times {3}^{x} - 3 = 0; \: a {}^{mn } = (a {}^{n} ) {}^{m} }$[/tex]
folosim substitutia t = 3^x
[tex]$\mathbf{ {t}^{2} + 2t - 3 = 0}$[/tex]
[tex]$\mathbf{ {t}^{2} + 3t - t - 3 = 0 \Longleftrightarrow \: t(t + 3) - (t + 3) = 0}$[/tex]
[tex]$\mathbf{(t + 3)(t - 1) = 0}$[/tex]
[tex]$\mathbf{t = - 3 \: \: }$[/tex]
[tex]$\mathbf{t = 1}$[/tex]
[tex]$\mathbf{ {3}^{x} = - 3 \:\Longrightarrow \: x \: nu \: apartine \: \mathbb{R}}$[/tex]
[tex]$\mathbf{ {3}^{x} = 1 \: \Longrightarrow \: {3}^{x {}^{} } = {3}^{0} \: \Longrightarrow \: x = 0}$[/tex]
[tex]$\mathbf{\Longrightarrow \:\boxed{\mathbf{x = 0 \: este \: singura \: solutie}}}$[/tex]
Bafta!
