Question

| 1-3x|=|3-2x|
Cum se rezolva asta?
Va rog ajutati-ma,dau 15 puncte.

Answer 1

$\big|1-3\text{x}\big|=\big|3-2\text{x}\big| \\ \\ \sqrt{(1-3\text{x})^2}= \sqrt{(3-2\text{x})^2}\Big|^2 \\ \\ \Big(\sqrt{(1-3\text{x})^2}\Big)^2 = \Big(\sqrt{(3-2\text{x})^2}\Big)^2 \\ \\ (1-3\text{x})^2 = (3-2\text{x})^2 \\ \\ 1^2-2\cdot 1\cdot 3\text{x} +(3\text{x})^2 = 3^2-2\cdot 3\cdot 2\text{x}-(2\text{x})^2 \\ \\ 1-6\text{x}+9\text{x}^2 = 9-12\text{x}+4\text{x}^2 \\ \\ 9\text{x}^2-4\text{x}^2-6\text{x}+12\text{x}+1-9 = 0 \\ \\ 5\text{x}^2+6\text{x}-8 = 0$

$\Delta = 6^2-4\cdot 5\cdot 8 = 36+160 = 196 = 14^2\\ \\ \text{x}_1 = \dfrac{-6- 14}{2\cdot 5} = \dfrac{-20}{10} = -2\\ \\ \text{x}_2 = \dfrac{-6+14}{2\cdot 5} = \dfrac{8}{10} \dfrac{4}{5}\\ \\ \Rightarrow \boxed{S=\Big\{-2, \dfrac{4}{5}\Big\}}$