Question

Решите уравнение (x+3)^3=9(x+3)

Answer 1

(x+3)³=9(x+3)

x³+9x²+27x+27=9x+27

x³+9x²+27x+27-9x-27=0

x³+9x²+18x=0

x(x²+9x+18)=0

x=0

x²+9x+18=0

x²+9x+18=0

D=9²-4*18=81-72=9=3²

$x_{1}= frac{-9- sqrt{9} }{2*1} = frac{-9-3}{2} = frac{-12}{3} =-6 \ x_{2}= frac{-9+ sqrt{9} }{2*1} = frac{-9+3}{2} = frac{-6}{2} =-3$

x₁= -6

x₂= -3

x₃=0