If x4-1210102024x4-1=0 then x =

x4-1 210102024 x4-1=0 2x+4x-24 x4-1=0 ⇒ 2x2+4x+4x-8-4=0 2x2+8x-12=0 x2+4x-6=0 x=-4±402 x=-2±10

If x4-1210102024x4-1=0 then x =

x4-1 210102024 x4-1=0 2x+4x-24 x4-1=0 ⇒ 2x2+4x+4x-8-4=0 2x2+8x-12=0 x2+4x-6=0 x=-4±402 x=-2±10

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If $[\begin{matrix} x & 4 & - 1 \end{matrix}] [\begin{matrix} 2 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & 2 & 4 \end{matrix}] [\begin{matrix} x \\ 4 \\ - 1 \end{matrix}] = 0$ then x =

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$- 1 + \sqrt{6}$

$8 \pm \sqrt{5}$

$- 2 \pm \sqrt{10}$

$3 \pm \sqrt{6}$

answer is C.

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Detailed Solution

$[\begin{matrix} x & 4 & - 1 \end{matrix}] [\begin{matrix} 2 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & 2 & 4 \end{matrix}] [\begin{matrix} x \\ 4 \\ - 1 \end{matrix}] = 0 [\begin{matrix} 2 x + 4 & x - 2 & 4 \end{matrix}] [\begin{matrix} x \\ 4 \\ - 1 \end{matrix}] = 0 \Rightarrow 2 x^{2} + 4 x + 4 x - 8 - 4 = 0 2 x^{2} + 8 x - 12 = 0 x^{2} + 4 x - 6 = 0 x = \frac{- 4 \pm \sqrt{40}}{2} x = - 2 \pm \sqrt{10}$