Question

solve each absolute value equation

9. |x^2-3x+3|=3

Answer 1

Solve

$$| \mathrm {x} ^ {2} - 3 \mathrm {x} + 3 | = 3$$ $$\left[ \begin{array}{l} x ^ {2} - 3 x + 3 = 3 \\ x ^ {2} - 3 x + 3 = - 3 \end{array} \right. = > \quad \left[ \begin{array}{l} x ^ {2} - 3 x = 0 \\ x ^ {2} - 3 x + 6 = 0 \end{array} \right. = > \quad \left[ \begin{array}{l} x _ {1} = 0, \quad x _ {2} = 3 \\ D < 0 \Rightarrow \text{no solution} \end{array} \right.$$

Answer: 0; 3