Question

[Wendy]

Giải phương trình 

a) x⁴ - 3x³ + 4x² - 3x - 1 = 0

b) 3x⁴ - 15x³ + 16x² - 13x + 2 = 0

c) x⁵ + 2x⁴ + 3x³  + 2x + 1 = 0

Answer 1

[ღᏠᎮღ🅼🅸🅽🅷ঔ🅽🅶ụ🆈ঌ__[ᴅʀᴇᴀм тᴇᴀм]__]

\(x^4-3x^3+4x^2-3x-1=0\)

\(\Leftrightarrow x^4+x^3+2x^3+2x^2+2x^2+2x+x+1=0\)

\(\Leftrightarrow x^3\left(x+1\right)+2x^2\left(x+1\right)+2x\left(x+1\right)+\left(x+1\right)=0\)
\(\Leftrightarrow\left(x^3+2x^2+2x+1\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left(x^3+2x^2+2x+1\right)\left(x+1\right)=0\)

\(\Leftrightarrow(x^3+x^2+x^2+x+x+1)\left(x+1\right)=0\)
\(\Leftrightarrow[x^2\left(x+1\right)+x\left(x+1\right)+\left(x+1\right)]\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2+x+1\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)^2\left(x^2+x+1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}(x+1)^2=0\\x^2+x+1=0\end{cases}}\Rightarrow\hept{\begin{cases}x+1=0\\\varnothing\end{cases}}\Rightarrow x=-1\)