Решите уравнение а)m^3+6m^2-m-6=0 б)x^3-5x^2-16x+80=0 в)1/8-1/4p-1/2p^2+p^3=0...

Question

Решите уравнение а)m^3+6m^2-m-6=0 б)x^3-5x^2-16x+80=0 в)1/8-1/4p-1/2p^2+p^3=0 г)27m-90=3m^3-10m^2

Answer 1

1)mˇ3 +6mˇ2 -m -6=0
  mˇ2(m+6) - (m+6) =0
(m+6)(mˇ2-1)=0
(m+6)(m+1)(m-1)=0
m1=-6,m2=-1,m3=1
2)xˇ3-5xˇ2-16x+80=0, xˇ2(x-5)-16(x-5)=0
(x-5)(xˇ2 -16)=0, (x-5)(x+4)(x-4)=0
x1=5,x2=-4, x3=4
3)1/8-1/4p -1/2pˇ2 +pˇ3=0
pˇ2(p-1/2)-1/4(p-1/2)=(p-1/2)(pˇ2-1/4)=(p-1/2)(p+1/2)(p-1/2)=
p1=1/2,p2=-1/2,p3=1/2=p1
4)27m-90=3mˇ3-10mˇ2
 mˇ2(3m-10)-9(3m-10)=0, (3m-10)(mˇ2-9)=0=(3m-10)(m+3)(m-3)=0
m1=10/3, m2=-3, m3=3