I would be happy to get some ideas on possible approaches to solve $$ x^3 - x^2 < 2x - 2\qquad (x \in \mathbb R). $$
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2Factorise it: $x^2(x-1)<2(x-1)$ i.e. $(x^2-2)(x-1)<0$ i.e. $(x-\sqrt{2})(x+\sqrt{2})(x-1)<0$. When is the product of three numbers negative? – Sep 15 '21 at 10:55
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1Factorise $x^3-x^2-2x+2$ and use wavy curve method. – Z Ahmed Sep 15 '21 at 10:56
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$$x^3-x^2-2x-2<0$$
$$(x-1)(x^2-2)<0$$
$$x\in (-\infty, -\sqrt2)\cup(1,\sqrt2)$$
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This question goes against our quality standard policy. Instead of posting an answer, you should encourage the person who posted the question to improve it. – José Carlos Santos Sep 15 '21 at 10:58
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