Решите уравнение 4(x^2+1) / (x^2+10x+1) - 5x/(x^2+1) + 3.5 = 0

[latex] frac{4(x^2+1)}{x^2+10+1}- frac{5x}{x^2+1} + frac{7}{2}=0\\ frac{ 4(frac{x^2+1}{x^2+1}) }{ frac{x^2+1+10x}{x^2+1} }- frac{5x}{x^2+1}+ frac{7}{2}=0\\ frac{4}{ 1+frac{10x}{x^2+1} } - frac{5x}{x^2+1}+ frac{7}{2}=0\\ frac{5x}{x^2+1}=t\\ frac{4}{1+2t}- frac{t}{1}+ frac{7}{2}=0\\ 8-2t-4t^2+7+14t=0\ -4t^2+12t+15=0\ 4t^2-12t-15=0\ D=144+240=384; sqrt{D}= sqrt{384}= sqrt{16 cdot 4cdot 6}=4 * sqrt{6}=8 sqrt{6}\\ t_{1/2}= frac{12pm 8 sqrt{6} }{8}=frac{3pm 2 sqrt{6} }{2} = frac{3}{2}+sqrt {6}[/latex]Обратная замена[latex] frac{5x}{x^2+1}= frac{3}{2} pm sqrt6\\ frac{5x}{x^2+1}= frac{3 pm 2sqrt 6}{2}\\ (x^2+1)(3pm2sqrt6)=10x\ 3pm2sqrt6)x^2-10x+(3pm2sqrt6)=0\ D=100-4(3pm2sqrt6)^2=100-4(9pm12sqrt6+24)=\ =100-36mp48sqrt6-96=-32mp48sqrt6\ D_1=-21-48sqrt6 extless 0; D_2=48sqrt6-32 extgreater 0\\ x_{1/2}= frac{10pm sqrt{48sqrt6-32}}{2(3-2sqrt6)}= frac{10pm 4 sqrt{3sqrt6-2}}{2 (3-2sqrt6)}= frac{5pm2sqrt{3sqrt6-2}}{3-2sqrt6} [/latex]