Question

Giải các phương trình:

\(a,8x^2-\left(4x+3\right)^3+\left(2x+3\right)^3=0\)

b, \(\left(x-2\right)\left(x+2\right)\left(x^2-10\right)=72\)

Answer 1

b) \(\left(x-2\right)\left(x+2\right)\left(x^2-10\right)=72\)

\(\Leftrightarrow\left(x^2-4\right)\left(x^2-10\right)=72\)

\(\Leftrightarrow t\left(t-6\right)=72\) ( với \(t=x^2-4\) \(\Rightarrow t\ge-4\forall x\) )

\(\Leftrightarrow t^2-6t-72=0\)

\(\Leftrightarrow t^2+6t-12t-72=0\)

\(\Leftrightarrow t\left(t+6\right)-12\left(t+6\right)=0\)

\(\Leftrightarrow\left(t-12\right)\left(t+6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t-12=0\\t+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}t=12\\t=-6\left(VL\right)\left(dot\ge-4\right)\end{matrix}\right.\)

\(\Leftrightarrow x^2-4=12\Leftrightarrow x^2=16\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)