Question

1) х^2/х+5=25/х+5 2) 2х^2/3х-5=х 3) х^3-64х=0 4) 3х^2-х+4=0 5) х-8/х-2=0

Answer 1

1)
$\frac{ {x}^{2} }{x + 5} = \frac{25}{x + 5} \: \: \: \: | \times (x + 5) \\ {x}^{2} = 25 \\ x = \sqrt{25} \\ x = 5$
2)
$\frac{2 {x}^{2} }{3x - 5} = x \: \: \: \: \: | \times (3x - 5) \\ 2 {x}^{2} = x(3x - 5) \\ 2 {x}^{2} = 3 {x}^{2} - 5x \\ 3 {x}^{2} - 2 {x}^{2} - 5x = 0 \\ {x}^{2} - 5x = 0 \\ x(x - 5) = 0 \\ x1 = 0 \\ x - 5 = 0\\ x2 = 5$
3)
${x}^{3} - 64x = 0 \\ x( {x}^{2} - 64) = 0 \\ x1 = 0 \\ - - - - - - \\ {x}^{2} - 64 = 0 \\ {x}^{2} = 64 \\ x2 = \sqrt{64} \\ x2 = 8$
4)
$3 {x}^{2} - x + 4 = 0 \\ d = 1 - 4 \times 3 \times 4 = 1 - 48 = - 47$
D<0, действительных корней нет, т.к. дискриминант меньше 0.

5)
$\frac{x - 8}{x - 2} = 0 \\ x - 8 = 0 \\ x = 8$
х ≠ 2 , т.к. делить на 0 нельзя