Question

решите уравнение:
1.(x+2)(x^2-2x+4)-x(x-3)(x+3)=26
2.(x-3)(x^2+3x+9)-x(x^2-16)=21
3.(2x-1)(4x^2+2x+1)=23+4x(2x^2-3)
4.16x(4x^2-5)+17=(4x+1)(16x^2-4x+1)

Answer 1

№1

$(x+2)(x^{2}-2x+4)-x(x-3)(x+3)=26\ (x^{3} -2x^{2} +4x+2x^{2} -4x+8)-x(x-3)(x+3)=26\ x^{3} -2x^{2} +4x+2x^{2} -4x+8-x(x^{2}-9)=26\ x^{3} -2x^{2} +4x+2x^{2} -4x+8-x^{3} +9x=26\ 8+9x=26\ 9x=26-8\ 9x=18\ x=2$

№2

$(x-3)(x^{2} +3x+9)-x(x^{2} -16)=21\ x^{3} +3x^{2} +9x-3x^{2} -9x-27-x^{3} +16x=21\ -27+16x=21\ 16x=21+27\ 16x=48\ x=3$

№3

$(2x-1)(4x^{2} +2x+1)=23+4x(2x^{2} -3)\ 8x^{3} +4x^{2} +2x-4x^{2} -2x-1=23+8x^{3} -12x\ 8x^{3} +4x^{2} +2x-4x^{2} -2x-8x^{3} +12x=23+1\ 12x=24\ x=2$

№4

$16x(4x^{2} -5)+17=(4x+1)(16x^{2} -4x+1)\ 64x^{3} -80x+17=64x^{3} -16x^{2} +4x+16x^{2} -4x+1\ 64x^{3} -64x^{3} +16x^{2} -16x^{2} -80x-4x+4x=1-17\ -80x=-16\ x=frac{1}{5}$