Question

Giải pt

(x + 2)³ + (3x - 1)(3x + 1) = (x + 1)³

Answer 1

Ta có

Pt <=> x³+6x²+12x+8+9x²-1=x³+3x²+3x+1

    <=> 12x²+9x+6=0

    <=> 3(4x²+3x+2)=0

<=>    \(3\left(4x^2+2.\frac{3}{4}.2x+2\right)=0\)

\(\Leftrightarrow3\left[\left(2x+\frac{3}{4}\right)^2+\frac{23}{16}\right]=0\)

\(\Leftrightarrow3\left(2x+\frac{3}{4}\right)^2+\frac{69}{16}=0\)vô lý vì \(3\left(2x+\frac{3}{4}\right)^2\ge0\Rightarrow3\left(2x+\frac{3}{4}\right)^2+\frac{69}{16}\ge\frac{69}{16}>0\)

^{Vậy pt vô ghiệm}