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