(x + 6)(x + 3)(x + 9)(x + 2) = 5x2
<=> (x2 + 9x + 18).(x2 + 11x + 18) = 5x2
<=> (x2 + 10x + 18 - x)(x2 + 10x + 18 + x) = 5x2
<=> (x2 + 10x + 18)2 - x2 = 5x2
<=> (x2 + 10x + 18)2 = 6x2
<=> \(\left[{}\begin{matrix}x^2+10x+18=\sqrt{6}x\\x^2+10x+18=-\sqrt{6}x\end{matrix}\right.\)
Với \(x^2+10x+18=\sqrt{6}x\Leftrightarrow x^2+\left(10-\sqrt{6}\right)x+18=0\)
\(\Delta=\left(10-\sqrt{6}\right)^2-72=34-20\sqrt{6}< 0\)
=> Phương trình vô nghiệm
Với \(x^2+10x+18=-\sqrt{6}x\Leftrightarrow x^2+\left(10+\sqrt{6}\right)x+18=0\)
\(\Delta=\left(10+\sqrt{6}\right)^2-72=34+20\sqrt{6}\) > 0
Phương trình có 2 nghiệm \(x=\dfrac{-10-\sqrt{6}\pm\sqrt{34+20\sqrt{6}}}{2}\)
\(\left(x+6\right)\left(x+3\right)\left(x+9\right)\left(x+2\right)=5x^2\)
\(\Leftrightarrow\left(x^2+3x+6x+18\right)\left(x^2+2x+9x+18\right)=5x^2\)
\(\Leftrightarrow\left(x^2+9x+18\right)\left(x^2+11x+18\right)=5x^2\)
\(\Leftrightarrow x^4+11x^3+18x^2+9x^3+99x^2+162x+18x^2+198x+324=5x^2\)
\(\Leftrightarrow x^4+20x^3+135x^2+360x+324=5x^2\)
\(\Leftrightarrow x^4+20x^3+130x^2+360x+324=0\)
\(\Leftrightarrow x\in\varnothing\)
