Question

1/(x-2)^2-1/x(x-4)=4/3

Answer 1

Ответ:

Объяснение:

$\displaystyle\\\frac{1}{(x-2)^2} -\frac{1}{x(x-4)} =\frac{4}{3} \\\\\\ODZ: x\neq 0;x\neq 2;x\neq 4\\\\\\\frac{1}{x^2-4x+4} -\frac{1}{x^2-4x}=\frac{4}{3} \\\\\\t=x^2-4x\\\\\\\frac{1}{t+4} -\frac{1}{t}=\frac{4}{3} \\\\\\3t-3(t+4)=4t(t+4)\\\\3y-3t-12=4t^2+16t\\\\4t^2+16t+12=0\\\\t^2+4t+3=0\\\\po\ Bieta\ t_1=-3;t_2=-1\\\\1)x^2-4x=-3\\\\x^2-4x+3=0\\\\po\ Bieta\ x_1=3;x_2=1\\\\\\2)x^2-4x=-1\\\\x^2-4x+1=0\\\\D=16-4=12\\\\x=2\pm\sqrt{3} \\\\\\Otvet:\{2\pm\sqrt{3};1;3\}$