Question

Tìm x: `(3x^2 -x+1)(3x^2 +5x+1)=27x^2`

Answer 1

\(\left(3x^2-x+1\right)\left(3x^2+5x+1\right)=27x^2\)

=>\(\left(3x^2+1-x\right)\left(3x^2+1+5x\right)=27x^2\)

=>\(\left(3x^2+1\right)^2+4x\left(3x^2+1\right)-5x^2-27x^2=0\)

=>\(\left(3x^2+1\right)^2+4x\left(3x^2+1\right)-32x^2=0\)

=>\(\left(3x^2+1+8x\right)\left(3x^2+1-4x\right)=0\)

=>\(\left(3x^2+8x+1\right)\left(3x-1\right)\left(x-1\right)=0\)

=>\(\left[{}\begin{matrix}3x^2+8x+1=0\\3x-1=0\\x-1=0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=1\\x=\dfrac{-4\pm\sqrt{13}}{3}\end{matrix}\right.\)