Question

Giải các phương trình sau :

a, \(x^4=24x+32\)

b, \(x^3=-3x^2+3x-1\)

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

Answer 1

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Answer 2

a/ \(\Leftrightarrow x^4-2x^3-4x^2+2x^3-4x^2-8x+8x^2-16x-32=0\)

\(\Leftrightarrow x^2\left(x^2-2x-4\right)+2x\left(x^2-2x-4\right)+8\left(x^2-2x-4\right)=0\)

\(\Leftrightarrow\left(x^2-2x-4\right)\left(x^2+2x+8\right)=0\)

\(\Leftrightarrow x^2-2x-4=0\Rightarrow x=1\pm\sqrt{5}\)

b/ \(2x^3=x^3-3x^2+3x-1\)

\(\Leftrightarrow2x^3=\left(x-1\right)^3\)

\(\Leftrightarrow x\sqrt[3]{2}=x-1\)

\(\Rightarrow x=\frac{1}{1-\sqrt[3]{2}}\)

c/ \(x^4-\left(x-1\right)^2=0\)

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

\(\Leftrightarrow x^2+x-1=0\Rightarrow x=\frac{-1\pm\sqrt{5}}{2}\)