Question

Решить уравнения: 1. 2x^2 +x-1=0 2. x^2 -9=0 3. x^2 -x=0 4.  5.   = 9-x

Answer 1

1.2x² +x-1=0
D=1-(-8)=9=3²
x₁=(-1+3)/4=2/4=0,5
x₂=(-1-3)/4=-4/4=-1
2.x² -9=0
x=√-(-9)=3
3.x² -x=0
x₁=0
x₂=1
4.$\frac{x^{2} -6}{x-3}= \frac{x}{x-3}$
$\frac{x^{2} -6}{x-3}-\frac{x}{x-3}=0$
$\frac{x^{2} -x-6}{x-3}=0$
$\left \{ {{x^{2} -x-6=0} \atop {x \neq 3}} \right.$
D=1-(-24)=25=5²
x₁=(1+5)/2=3
$x \neq 3$           
x₂(1-5)/2=-2
x=-2
5.$\frac{20}{x} =9-x$
$\frac{20}{x}-9+x=0$
$\frac{20-9x+x^{2} }{x}=0$
$\left \{ {{ x^{2} -9x+20=0} \atop {x \neq 0}} \right.$
D=81-80=1²
x₁=(9+1)/2=5
x₂=(9-1)/2=4