Question

решить уравнение 3/х-5+8/х=2 ​

Answer 1

Ответ:

домножить на x(x-5)

3x+8(x-5)=2x(x-5)

11x-40=2x^2-10x

2x^2-21x+40=0

D=21^2-320=121=11^2

x=(21±11)/4=8 и 2,5

Answer 2

$\frac{3}{x - 5} + \frac{8}{x} = 2 \\ \frac{3}{x - 5} + \frac{8}{x} - 2 = 0 \\ \frac{3x + 8(x - 5) - 2x(x - 5)}{x(x - 5)} = 0 \\ \frac{3x + 8x - 40 - {2x}^{2} + 10x}{x(x - 5)} = 0 \\ \frac{ - {2x}^{2} + 21x - 40}{x(x - 5)} = 0 \\ \\ - {2x}^{2} + 21x - 40 = 0 \\ D = {b}^{2} - 4ac \\ \\ a = - 2 \\ b = 21\\ c = - 40 \\ \\ D = {21}^{2} - 4 \times ( - 2) \times ( - 40) = 441 - 320 \\ \\ x_{1} = \frac{ \sqrt{D} - b}{2a} = \frac{ \sqrt{121} - 21}{2 \times ( - 2)} = \frac{5}{2} = 2.5 \\ x_{2} = \frac{ - \sqrt{D} - b}{2a} = \frac{ - \sqrt{121} - 21}{2 \times ( - 2)} = 8$

Ответ : х1 = 5/2; х2 = 8