Minimum value of (x + 1) (x + 2) (x + 3) (x + 4) + 2 is ___

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Solution

$G . E . = (x^{2} + 5 x + 5)^{2} + 1 \geq 1$

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Minimum value of (x + 1) (x + 2) (x + 3) (x + 4) + 2 is ______________

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∣ ∣ ∣ \begin{matrix} x + 1 & x - 1 x - 3 & x + 2 \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 4 & - 1 1 & 3 \end{matrix} ∣ ∣ ∣

|\begin{matrix} x + 1 & x - 1 \\ x - 3 & x + 2 \end{matrix}| = |\begin{matrix} 4 & - 1 \\ 1 & 3 \end{matrix}|

(x + 1) (x + 2) (x + 3) (x + 4) = 24

∣ ∣ ∣ \begin{matrix} x + 1 & x - 1 x - 3 & x + 2 \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 4 & - 1 1 & 3 \end{matrix} ∣ ∣ ∣

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