Question

решить уравнение lx^2+x-1l = 2x-1

Answer 1

$|x^{2}+x-1|=2x-1\\\\1)2x-1\geq 0\\\\2x\geq1\\\\x\geq0,5$

$2)\left[\begin{array}{ccc}x^{2}+x-1=2x-1 \\x^{2}+x-1=1-2x \end{array}\right\\\\\left[\begin{array}{ccc}x^{2}-x=0 \\x^{2}+3x-2=0 \end{array}\right\\\\x^{2}-x=0\\\\x(x-1)=0\\\\x_{1} =0\\\\x_{2}=1$

x = 0 - не уд. , так как x ≥ 0,5

$x^{2}+3x-2=0\\\\D=3^{2}-4*(-2)=9+8=17\\\\x_{3}=\frac{-3+\sqrt{17}}{2}\\\\x_{4}=\frac{-3-\sqrt{17}}{2}-neyd\\\\Otvet:\boxed{\frac{\sqrt{17}-3 }{2};1}$