Question

Найдите корни уравнения 6x/x-4=x+4

Answer 1

$\frac{6x}{x-4} =x+4 \\ \\ \frac{6x}{x-4} -x-4=0 \\ \\ \frac{6x}{x-4} - \frac{x+4}{1} =0 \\ \\ \frac{6x}{x-4} - \frac{(x+4)(x-4)}{x-4} =0 \\ x-4 \neq 0 \\ 6x-( x^{2} -16)=0 \\ 6x- x^{2} +16=0 \\ - x^{2} +6x+16=0$

$x^{2} -6x-16=0\\D=36+64=100 \\ \sqrt{D} =10 \\ x_{1} = \frac{6+10}{2} = \frac{16}{2} =8 \\ x_{2} = \frac{6-10}{2} = \frac{-4}{2} =-2$

Answer 2

6х/(х-4)=х+4
6х=(х-4)*(х+4)
6х=х²-16
х²-6х-16=0
Д=36+64=100, √Д=+ 10
х₁=(6+10)/2=8
х₂=(6-10)/2= -2.