x^11 x^9+x^7 x^5 lt;0 x^9(x^2 1)+x^5(x^2 1) lt;0 (x^9+x^5)(x^2 1) lt;0 x^5(x^4+1)(x^2 1) lt;0 x^5(x^2 1) lt;0 x^5(x 1)(x ...

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Integration by Substitution

Solve x11-x...

Question

Solve $x^{11} - x^{9} + x^{7} - x^{5} < 0$

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Solution

$x^{11} - x^{9} + x^{7} - x^{5} < 0$
$x^{9} (x^{2} - 1) + x^{5} (x^{2} - 1) < 0$
$(x^{9} + x^{5}) (x^{2} - 1) < 0$
$x^{5} (x^{4} + 1) (x^{2} - 1) < 0$
$x^{5} (x^{2} - 1) < 0$
$x^{5} (x - 1) (x + 1) < 0$
$∴ x \in (- \infty, - 1) \cup (0, 1)$

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