Question

5. (66) Решите уравнение: |4х² +4х|-1=0​

Answer 1

$\left | 4x^2+4x \right |-1=0\Leftrightarrow \left | 4x^2+4x \right |=1\Leftrightarrow \left ( 4x^2+4x \right )^2=1^1$

$\left ( 4x^2+4x-1 \right )\left ( 4x^2+4x+1 \right )=0\Leftrightarrow \left ( (2x+1)^2-2 \right )(2x+1)^2=0\Rightarrow x=\left \{ -\frac{1}{2},-\frac{1}{2}\pm\frac{1}{\sqrt{2}} \right \}$