Category: Algebra

Question Number 183381 by Shrinava last updated on 25/Dec/22 $$\frac{{3\mathrm{n}}^5+{4\mathrm{n}}^4-{7\mathrm{n}}^3+{5\mathrm{n}}^2-5}{\mathrm{n}+1}$$$$\mathrm{There}\mathrm{can}\mathrm{be}\mathrm{no}\mathrm{residue}:$$$$\mathrm{a})0\mathrm{b})2\mathrm{c})4\mathrm{d})5\mathrm{e})9$$ Commented by Shrinava last updated…

Question Number 117828 by redouaneee last updated on 13/Oct/20 $$1)(\sqrt{3}-1)(\sqrt{3}+1)=\sqrt{3}\times \sqrt{3}-\sqrt{3}-1$$$$=3-\sqrt{3}-1$$$$=2-\sqrt{3}$$$$2)(2x+\sqrt{3})(2x-\sqrt{3})={\left(2x\right)}^2-2x\sqrt{3}+2x\sqrt{3}-3$$$$=4x^2-3$$ Answered by MJS_new…

Question Number 183363 by Shrinava last updated on 25/Dec/22 $$\mathrm{Find}:$$$$2003\cdot {2005}^3-2004\cdot {2002}^3$$ Answered by Frix last updated on 25/Dec/22 $$\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{3}} −\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}−\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{3}} =\mathrm{8}{x}^{\mathrm{3}}…

Question Number 183353 by Spillover last updated on 25/Dec/22 $$Forthefunction$$$$f\left(x\right)=\{\begin{array}{l}{x}^2-3ifx<4\\ \frac{x^2}{x+4}ifx⩾4\end{array}$$$$Find\left(i\right)\underset{x\to -4}{\lim }f\left(x\right)ii)\underset{x\to +4}{\lim }f\left(x\right)$$ Answered by TheSupreme last updated…

Question Number 52282 by Tawa1 last updated on 05/Jan/19 $$\mathrm{Find}\mathrm{the}\mathrm{range}\mathrm{of}\mathrm{values}\mathrm{of}\mathrm{x}$$$$\mid \frac{\mathrm{x}-1}{2\mathrm{x}}\mid ⩾{\mathrm{x}}^2+1$$ Commented by tanmay.chaudhury50@gmail.com last updated on 05/Jan/19 Commented by tanmay.chaudhury50@gmail.com…