Question

Determine as raízes reais da equação |x²-3x+2| = |2x-11|

Answer 1

$|x^2-3x+2|=|2x-11|\\ \\ x^2-3x+2=2x-11\quad ou\quad x^2-3x+2=-2x+11\\ \\ x2-3x+2-2x+11=0\\ x^2-5x+13\\ \\ \Delta =b^2-4ac\\ \Delta =(-5)^2-4*1*13\\ \Delta =25-42\\ \Delta =-14\\ \\ x^2-3x+2=-2x+11\\ x^2-3x+2+2x-11=0\\ x^2-x-9=0\\ \\ \Delta =b^2-4ac\\ \Delta =(-1)^2-4*1*(-9)\\ \Delta =1+36\\ \Delta =37\\ \\ \frac { -b\pm \sqrt { 37 } }{ 2a } \\ x^1=\frac { 1+\sqrt { 37 } }{ 2 } \\ x^2=\frac { 1-\sqrt { 37 } }{ 2 }$

${S=\{ \frac { 1+\sqrt { 37 } }{ 2 } ,\quad \frac { 1-\sqrt { 37 } }{ 2 } \}$