Question Number 193087 by Abdullahrussell last updated on 03/Jun/23 Answered by Frix last updated on 03/Jun/23 $${x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −\mathrm{4}{x}−\mathrm{2} \\ $$$$\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{4}} −\frac{\mathrm{3}}{\mathrm{2}}\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} −\mathrm{3}\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)−\frac{\mathrm{3}}{\mathrm{16}} \\ $$$$\left(\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 127547 by Mathgreat last updated on 30/Dec/20 Answered by mr W last updated on 31/Dec/20 Commented by mr W last updated on 31/Dec/20…
Question Number 127525 by Mathgreat last updated on 30/Dec/20 Commented by Mathgreat last updated on 30/Dec/20 $$\boldsymbol{{x}}_{\mathrm{1}} +\boldsymbol{{x}}_{\mathrm{2}} +\boldsymbol{{x}}_{\mathrm{3}} +…+\boldsymbol{{x}}_{\boldsymbol{{n}}} =\:??? \\ $$ Commented by…
Question Number 127519 by O Predador last updated on 30/Dec/20 Answered by mahdipoor last updated on 30/Dec/20 $$\mathrm{0}.\mathrm{0833}…=\mathrm{0}.\mathrm{08}\overset{−} {\mathrm{3}}=\mathrm{0}.\mathrm{08}+\mathrm{0}.\mathrm{00}\overset{−} {\mathrm{3}}= \\ $$$$\frac{\mathrm{8}}{\mathrm{100}}+\frac{\mathrm{1}}{\mathrm{300}}=\frac{\mathrm{25}}{\mathrm{300}}=\frac{\mathrm{1}}{\mathrm{12}}=\frac{\mathrm{1}×\mathrm{2}}{\mathrm{1}×\mathrm{2}×\mathrm{3}×\mathrm{4}}=\frac{\mathrm{2}!}{\mathrm{4}!}=\frac{\left[{log}_{\mathrm{2}} \left({x}^{\mathrm{2}} \right)−\mathrm{2}\right]!}{\left[{log}_{\mathrm{2}} \left({x}\right)+\mathrm{2}\right]!}…
Question Number 193049 by Mingma last updated on 02/Jun/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 193045 by Trent1111 last updated on 02/Jun/23 $${what}\:{is}\:{the}\:{HCF}\:{of}\: \\ $$$$\mathrm{8}{k}+\mathrm{1}\:{and}\:\mathrm{9}{k}\:?\:{where}\:{k}\:\in\:\mathbb{Z}^{+} \\ $$ Answered by MM42 last updated on 02/Jun/23 $$\left(\mathrm{8}{k}+\mathrm{1},\mathrm{9}{k}\right)={d} \\ $$$${d}\mid\mathrm{8}{k}+\mathrm{1}\:\Rightarrow{d}\mid\mathrm{72}{k}+\mathrm{9}\:\:\: \\…
Question Number 127500 by mr W last updated on 30/Dec/20 $${if}\:\mathrm{sin}\:{x}_{\mathrm{1}} +\mathrm{sin}\:{x}_{\mathrm{2}} +…+\mathrm{sin}\:{x}_{\mathrm{100}} =\mathrm{0}, \\ $$$${find}\:{the}\:{maximum}\:{value}\:{of} \\ $$$$\mathrm{sin}^{\mathrm{5}} \:{x}_{\mathrm{1}} +\mathrm{sin}^{\mathrm{5}} \:{x}_{\mathrm{2}} +…+\mathrm{sin}^{\mathrm{5}} \:{x}_{\mathrm{100}} . \\…
Question Number 193026 by Mingma last updated on 02/Jun/23 Answered by aleks041103 last updated on 02/Jun/23 $$\left(\mathrm{3}+\sqrt{\mathrm{5}}\right)^{\mathrm{3}} =\mathrm{3}^{\mathrm{3}} +\mathrm{3}×\mathrm{3}^{\mathrm{2}} ×\sqrt{\mathrm{5}}+\mathrm{3}×\mathrm{3}×\mathrm{5}+\mathrm{5}\sqrt{\mathrm{5}}= \\ $$$$=\mathrm{27}+\mathrm{45}+\mathrm{32}\sqrt{\mathrm{5}}=\mathrm{72}+\mathrm{32}\sqrt{\mathrm{5}} \\ $$$$\mathrm{32}\sqrt{\mathrm{5}}=\sqrt{\mathrm{5}×\mathrm{32}^{\mathrm{2}} }=\sqrt{\mathrm{5}×\mathrm{1024}}=\sqrt{\mathrm{5120}}=\mathrm{71}+{r}…
Question Number 127481 by Mathgreat last updated on 30/Dec/20 Commented by hknkrc46 last updated on 30/Dec/20 $${g}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{1}\:\Rightarrow\:{g}^{−\mathrm{1}} \left({x}\right)\:=\:\sqrt[{\mathrm{3}}]{{x}\:−\:\mathrm{1}} \\ $$$${f}\left({x}^{\mathrm{3}} \:+\:\mathrm{1}\right)\mid_{\sqrt[{\mathrm{3}}]{{x}\:−\:\mathrm{1}}} \:=\:\left({x}^{\mathrm{5}} \:+\:\mathrm{4}{x}\:+\:\mathrm{2}\right)\mid_{\sqrt[{\mathrm{3}}]{{x}\:−\:\mathrm{1}}} \\…
Question Number 61937 by Tawa1 last updated on 12/Jun/19 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{n}^{\mathrm{3}} \:+\:\mathrm{5}}{\mathrm{n}!} \\ $$ Commented by mr W last updated on 12/Jun/19 $${seems}\:{to}\:{be}\:\mathrm{10}{e}. \\…