Question

Решите ! 1.чему равен корень уравнения: 1) х-8/х+2 = 7/3 2) 4/х-1,2 = 15/х-10 / - значит дробь. 2.найдите корень уравнения: 1) х/3 + х/12 = 15/4. 2) 7х/9 - 3х/4 = 5/12. 3) 1 - 8х/15 = 4х/9. / - значит дробь.

Answer 1

$1.\\ 1)\\ x - \frac{8}{x} + 2 = \frac{7}{3} \\ x - \frac{8}{x} + 2 - \frac{7}{3} = 0 \\ x - \frac{8}{x} - \frac{1}{3} = 0 \\ 3x^2 - x - 24 = 0 \\ (x \neq 0) \\ D = 1 + 4*3*24 = 289 \\ x_{1} = \frac{1-17}{2*3} = -\frac{8}{3} \\ x_{2} = \frac{1-17}{2*3} = 3 \\$

$\\ 2) \frac{4}{x}-1,2 = \frac{15}{x} - 10 \\ \frac{4}{x}-1,2 - \frac{15}{x} + 10 = 0 \\ -\frac{11}{x}+8,8= 0 \\ -11+8,8x= 0 \\ 8,8x = 11 \\ x = \frac{11}{8,8} \\ x = 1,25$

$2. \\ 1)\\ \frac{x}{3}+\frac{x}{12}=\frac{15}{4} \\ \frac{4x+x}{12}=\frac{15}{4} \\ \frac{5x}{12}=\frac{15}{4} \\ 20x = 180 x = 9 \\ \\ 2) \\ \frac{7x}{9}-\frac{3x}{4}=\frac{5}{12} \\ \frac{28x-27x}{36}=\frac{5}{12} \\ \frac{x}{36}=\frac{15}{36} \\ x=15 \\ \\ 3)\\ 1 - \frac{8x}{15}=\frac{4x}{9} \\ 1 - \frac{8x}{15}-\frac{4x}{9} = 0\\ \frac{45-24x-20x}{45} = 0\\ 45-4x = 0\\ 4x = 45\\ x =11\frac{1}{4}\\$