Question

[Dưa Trong Cúc]

Giải các phương trình sau

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

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

c,\(2x^3+7x^2+7x+2=0\)

Answer 1

[Lê Thị Hồng Vân]

\(a,x^4+2x^3-3x^2-8x-4=0\\ \Leftrightarrow x^4+x^3+x^3+x^2-4x^2-4x-4x-4=0\\ \Leftrightarrow x^3\left(x+1\right)+x^2\left(x+1\right)-4x\left(x+1\right)-4\left(x+1\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x^3+x^2-4x-4\right)=0\\ \Leftrightarrow\left(x+1\right)\left[x^2\left(x+1\right)-4\left(x+1\right)\right]=0\\ \Leftrightarrow\left(x+1\right)\left(x+1\right)\left(x^2-4\right)=0\\ \Leftrightarrow\left(x+1\right)^2\left(x-2\right)\left(x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+1=0\\x+2=0\\x-2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-2\\x=2\end{matrix}\right.\\ Vậy.....\)

\(b,\left(x-2\right)\left(x+2\right)\left(x^2-10\right)=72\\ \Leftrightarrow\left(x^2-4\right)\left(x^2-10\right)=72\\ \Leftrightarrow\left(x^2-7+3\right)\left(x^2-7-3\right)=72\\ \Leftrightarrow\left(x^2-7\right)^2-9=72\\ \Leftrightarrow\left(x^2-7\right)^2=81\\ \Rightarrow\left[{}\begin{matrix}x^2-7=9\\x^2-7=-9\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=\sqrt{-2}\left(vôlí\right)\end{matrix}\right.\\ Vậyx=\sqrt{2}\)

\(c,2x^3+7x^2+7x+2=0\\ \Leftrightarrow2x^3+2x^2+5x^2+5x+2x+2=0\\ \Leftrightarrow2x^2\left(x+1\right)+5x\left(x+1\right)+2\left(x+1\right)=0\\ \Leftrightarrow\left(x+1\right)\left(2x^2+5x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+1=0\\2x^2+5x+2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=?\left(tựtính\right)\end{matrix}\right.\)