Question

Am nevoie doar de rezolvarea punctelor a și c vă rog mult!!​

Answer 1

Răspuns:

Explicație pas cu pas:

conditie: x ≠ 0

notam:

$\lg x = t$

a)

$t^{2} + 4t + 3 = 0$

$(t + 1)(t + 3) = 0$

$t_{1} = - 1 \iff \lg x = -1 \iff x_{1} = 10^{-1} \iff x_{1} = \dfrac{1}{10}$

$t_{2} = - 3 \iff \lg x = -3 \iff x_{2} = 10^{-3} \iff x_{2} = \dfrac{1}{1000}$

c)

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

$t(2t^{2} + 3t - 2) = 0 \iff 2(2t - 1)(t + 2) = 0$

$t_{1} = 0 \iff \lg x = 0 \iff x_{1} = 10^{0} \implies x_{1} = 1$

$t_{2} = \dfrac{1}{2} \iff \lg x = \dfrac{1}{2} \iff x_{2} = 10^{\frac{1}{2}} \implies x_{2} = \sqrt{10}$

$t_{3} = - 2 \iff \lg x = - 2 \iff x_{3} = 10^{-2} \implies x_{3} = \dfrac{1}{100}$