\(\left(x^2+x\right)^2+4\left(x^2+x\right)=12\)
Đặt \(a=x^2+x\)
\(\Leftrightarrow a^2+4a=12\)
\(\Leftrightarrow a^2+4a-12=0\)
\(\Leftrightarrow a^2+6a-2a-12=0\)
\(\Leftrightarrow a\left(a+6\right)-2\left(a+6\right)=0\)
\(\Leftrightarrow\left(a+6\right)\left(a-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}a=-6\\a=2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x^2+x=-6\\x^2+x=2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x^2+2\cdot x\cdot\frac{1}{2}+\frac{1}{4}+\frac{23}{4}=0\\x^2+2x-x-2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x+\frac{1}{2}\right)^2=\frac{-23}{4}\left(loai\right)\\\left(x+2\right)\left(x-1\right)=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-2\\x=1\end{cases}}\)
Vậy....
\(\left(x^2+6x+10\right)^2+\left(x+3\right)\left(3x^2+20x+36\right)=0\)
( rút gọn phá ngoặc tất cả )
\(\Leftrightarrow x^4+15x^3+85x^2+216x+208=0\)
\(\Leftrightarrow x^4+4x^3+11x^3+44x^2+41x^2+164x+52x+208=0\)
\(\Leftrightarrow x^3\left(x+4\right)+11x^2\left(x+4\right)+41x\left(x+4\right)+52\left(x+4\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x^3+11x^2+41x+52\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x^3+4x^2+7x^2+28x+13x+52\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left[x^2\left(x+4\right)+7x\left(x+4\right)+13\left(x+4\right)\right]=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+4\right)\left(x^2+7x+13\right)=0\)
\(\Leftrightarrow\left(x+4\right)^2\left(x^2+2\cdot x\cdot\frac{7}{2}+\frac{49}{4}+\frac{3}{4}\right)=0\)
\(\Leftrightarrow\left(x+4\right)^2\left[\left(x+\frac{7}{2}\right)^2+\frac{3}{4}\right]=0\)
\(\Leftrightarrow x+4=0\)
\(\Leftrightarrow x=-4\)
Vậy....
