Question

Tìm x:

( x²+8x+12 )( x²-7x+12 ) = 16x²

Answer 1

Lời giải:
Đặt \(x^2+12=a\). Khi đó PT trở thành:

\((a+8x)(a-7x)=16x^2\)

\(\Leftrightarrow a^2+ax-56x^2=16x^2\)

\(\Leftrightarrow a^2+ax-72x^2=0\)

\(\Leftrightarrow a^2+9ax-8ax-72x^2=0\)

\(\Leftrightarrow a(a+9x)-8x(a+9x)=0\)

\(\Leftrightarrow (a+9x)(a-8x)=0\Rightarrow \left[\begin{matrix} a+9x=0\\ a-8x=0\end{matrix}\right.\)

Nếu \(a+9x=0\Leftrightarrow x^2+12+9x=0\)

\(\Leftrightarrow (x+\frac{9}{2})^2=\frac{33}{4}\Rightarrow x=\pm \frac{\sqrt{33}}{2}-\frac{9}{2}\)

Nếu \(a-8x=0\Leftrightarrow x^2+12-8x=0\)

\(\Leftrightarrow (x-6)(x-2)=0\Rightarrow \left[\begin{matrix} x=6\\ x=2\end{matrix}\right.\)

Vậy...........