Question

Giải các phương trình :

a, 3x³  + 2x²  + 2x + 3 = 0

Answer 1

a, 3x³  + 2x²  + 2x + 3 = 0

<=>3x³+3+2x²+2x=0

<=>3(x³+1)+2x.(x+1)=0

<=>3.(x+1)(x²-x+1)+2x.(x+1)=0

<=>(x+1)[3.(x²-x+1)+2x]=0

<=>(x+1)(3x²-3x+3+2x)=0

<=>(x+1)(3x²-x+3)=0

mà 3x²-x+3=3.(x²-\(\frac{1}{3}\)x+1)

=3.(x²-2.x.\(\frac{1}{6}\)+\(\frac{1}{36}+\frac{35}{36}\))

=3.(x²-2.x.\(\frac{1}{6}+\frac{1}{36}\))\(+\frac{35}{12}\)

=3.(x-\(\frac{1}{6}\))²+\(\frac{35}{12}\ge0\left(\text{vì (x-}\frac{1}{6}\text{)}\ge0\right)\)

nên x+1=0

<=>x=-1