Question

Stie cimeva cum se rezolva ? √3x-5=2

Answer 1

√3x-5=2
√3x=2+5
√3x=7
x=7/√3
x=7/1,73
x=4,06

Answer 2

$\sqrt{3x-5} = 2,\quad 3x-5 \geq 0 \Rightarrow 3x \geq 5 \Rightarrow x \geq \dfrac{5}{3} \Rightarrow D = \Big[\dfrac{5}{3} , \infty\Big) \\ \\ \sqrt{3x-5} = 2 \Big|^2 \Rightarrow \Big(\sqrt{3x-5} \Big)^2 = 2^2 \Rightarrow |3x-5| = 4 \Rightarrow 3x-5 = \pm 4 \\ \\ \boxed{1} \quad 3x-5 = 4 \Rightarrow 3x = 4+5 \Rightarrow 3x = 9 \Rightarrow x = 3 \in D \\ \boxed{2} \quad 3x-5 = -4 \Rightarrow 3x = -4+5 \Rightarrow 3x = 1 \Rightarrow x = \dfrac{1}{3}\notin D$

$\Rightarrow \boxed{S = \Big\{3\Big\} }$