Question

X⁴ + 4 = 5X( X² - 2)

Answer 1

\(x^4+4=5x\left(x^2-2\right)\)

\(\Leftrightarrow x^4-5x^3+10x+4=0\)

\(\Leftrightarrow\left(x+1\right)\left(x^3-6x^2+6x+4\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\left(x^2-4x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-2=0\\x^2-4x-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\\x=2\pm\sqrt{6}\end{matrix}\right.\)

Answer 2

\(X^4+4=5X\left(X^2-2\right)\\ \Leftrightarrow X^4-5X^3+10X+4=0\\ \Leftrightarrow\left(X+1\right)\left(X-2\right)\left(X^2-4X-2\right)\)

\(\left[{}\begin{matrix}X+1=0\\X-2=0\\X^2-4X-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}X=-1\\X=2\\X=2+\sqrt{6}\\X=2-\sqrt{6}\end{matrix}\right.\)

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