Question

Решить уравнения:
а) (2x-5)^4 = 8(2х-5)
б) (х+1)(х^2+4х+4)=30(х+2)

Answer 1

а)
$(2x - 5) = y \\ y^{4} = 8y \\ {y}^{4} - 8y = 0 \\ y( {y}^{3} - 8) = 0 \\ y(y - 2)(y^{2} + 2y + 4) = 0 \\ 1)y = 0 \\ 2)y = 2 \\ 3){y}^{2} + 2y + 4 = 0 \\ d = 4 - 16 = - 12 \\ 1)2x - 5 = 0 \\ 2x = 5 \\ x = 2.5 \\ 2)2x - 5 = 2 \\ 2x = 7 \\ x = 3.5$
Ответ: x = 2.5, 3.5