Question

Решите(Через дискриминат)
25.18

Answer 1

а) $6x (2x+1)=5x+1 \\ 12x^2+6x-5x-1=0 \\ 12x^2+x-1=0 \\ D=1-4*12*(-1)=1+48=49=7^2 \\ x_1=\frac {-1+7}{24}=\frac {1}{4} \\ x_2=\frac {-1-7}{24}= -\frac {1}{3}$

б) $2x (x-8)=-x-18 \\ 2x^2-16x+x+18=0 \\ 2x^2-15x+18=0 D=225-4*2*18=225-144=81=9^2 \\ x_1=\frac {15+9}{4}=6 \\ x_2=\frac {15-9}{4}=1.5$

в)
$8x (1+2x)=-1 \\ 8x +16x^2+1=0 \\ 16x^2 +8x+1=0 \\ D=64-4*16=64-64=0 \\ x=\frac {-8\pm0}{32}=\frac {1}{4}= 0.25$

г)
$x (x-5)=1-4x \\ x^2-5x-1+4x=0 \\ x^2-x-1=0 \\ D=1-4*(-1)=1+4=5 \\ x_1=\frac {1+\sqrt {5}}{2} \\ x_2=\frac {1-\sqrt {5}}{2}$