Solution set of $(x^{2} - 1) (x^{3} - 1) (x^{4} - 1) > 0$ is

(1, \infty)

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(- 1, \infty)

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[1, \infty)

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[- 1, \infty)

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Solution

The correct option is A $(1, \infty)$
$(x^{2} - 1) (x^{3} - 1) (x^{4} - 1) > 0 \Rightarrow (x + 1) (x - 1) (x - 1) (x^{2} + x + 1) (x + 1) (x - 1) (x^{2} + 1) > 0 \Rightarrow (x^{2} + 1) (x^{2} + x + 1) (x + 1)^{2} (x - 1)^{3} > 0 \Rightarrow (x - 1)^{3} > 0 \Rightarrow x > 1$

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