Question

7. Rezolvaţi 3^2x + 2•3^x - 3 = 0.​

Answer 1

Răspuns:

$\mathbf{x = 0}$

Explicație pas cu pas:

$\mathbf{3 {}^{2x} + 2 \times 3 {}^{x} - 3 = 0 }$

$\mathbf{( {3}^{x} ) {}^{2} + 2 \times {3}^{x} - 3 = 0; \: a {}^{mn } = (a {}^{n} ) {}^{m} }$

folosim substitutia t = 3^x

$\mathbf{ {t}^{2} + 2t - 3 = 0}$

$\mathbf{ {t}^{2} + 3t - t - 3 = 0 \Longleftrightarrow \: t(t + 3) - (t + 3) = 0}$

$\mathbf{(t + 3)(t - 1) = 0}$

$\mathbf{t = - 3 \: \: }$

$\mathbf{t = 1}$

$\mathbf{ {3}^{x} = - 3 \:\Longrightarrow \: x \: nu \: apartine \: \mathbb{R}}$

$\mathbf{ {3}^{x} = 1 \: \Longrightarrow \: {3}^{x {}^{} } = {3}^{0} \: \Longrightarrow \: x = 0}$

$\mathbf{\Longrightarrow \:\boxed{\mathbf{x = 0 \: este \: singura \: solutie}}}$

Bafta!