Question Number 77800 by mr W last updated on 10/Jan/20 $${if}\:{a}_{\mathrm{1}} =\mathrm{1},\:{a}_{\mathrm{2}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}} =\sqrt{{a}_{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} }\:{with}\:{n}\geqslant\mathrm{3} \\ $$$${find}\:{a}_{{n}} \:{in}\:{explicit}\:{form}. \\ $$ Terms of…
Question Number 77799 by mr W last updated on 10/Jan/20 $${if}\:{a}_{\mathrm{1}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}+\mathrm{1}} =\mathrm{3}{a}_{{n}} +\mathrm{6}{n}^{\mathrm{2}} −\mathrm{12}{n}+\mathrm{2} \\ $$$${find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$ Answered by mr…
Question Number 143329 by Huy last updated on 13/Jun/21 $$\mathrm{log}_{\mathrm{2x}+\mathrm{1}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{log}_{\mathrm{x}+\mathrm{1}} \left(\mathrm{3}\sqrt{\mathrm{2x}+\mathrm{5}}+\mathrm{18}\right)=\mathrm{2x} \\ $$ Answered by Olaf_Thorendsen last updated on 13/Jun/21 $$\mathrm{log}_{\mathrm{2}{x}+\mathrm{1}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{log}_{{x}+\mathrm{1}}…
Question Number 12261 by frank ntulah last updated on 17/Apr/17 $${find}\:{the}\:{value}\:{of}\:{a}\:{b}\:{and}\:{c} \\ $$$$\:{a}+{b}+{c}=\mathrm{4} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{66} \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{280} \\ $$…
Question Number 12257 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Answered by sma3l2996 last updated on 17/Apr/17 $$\left({a}+{b}−\mathrm{2}{ab}\right)^{\mathrm{2}} +\left({a}+{b}−\mathrm{1}\right)^{\mathrm{2}} =\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{4}{a}^{\mathrm{2}} {b}^{\mathrm{2}} −\mathrm{4}{ab}^{\mathrm{2}} +\mathrm{2}{a}\left({b}−\mathrm{2}{ab}\right)\right)+\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 12255 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Answered by mrW1 last updated on 16/Apr/17 $$\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)\left({x}+\mathrm{4}\right)+\mathrm{1} \\ $$$$=\left({x}+\frac{\mathrm{5}}{\mathrm{2}}−\frac{\mathrm{3}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{2}}\right)+\mathrm{1} \\ $$$$=\left[\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} \right]\left[\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \right]+\mathrm{1}…
Question Number 12254 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143322 by enter last updated on 13/Jun/21 Answered by mr W last updated on 13/Jun/21 Commented by mr W last updated on 13/Jun/21…
Question Number 143320 by mathdanisur last updated on 12/Jun/21 $${prove}\:{that}:\:\:{tan}^{\mathrm{2}} \mathrm{36}°\:+\:{tan}^{\mathrm{2}} \mathrm{72}°\:=\:\mathrm{5} \\ $$ Answered by Ar Brandon last updated on 12/Jun/21 $$\mathrm{tan}^{\mathrm{2}} \mathrm{36}°+\mathrm{tan}^{\mathrm{2}} \mathrm{72}°=\mathrm{tan}^{\mathrm{2}}…
Question Number 143293 by Huy last updated on 12/Jun/21 $${f}\left({x}\right)={ln}\left(\mathrm{1}+{ln}\left({x}\right)\right). \\ $$$${f}\left({x}\right)={ln}\left({f}'\left({x}\right)\right).{Find}\:{x} \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $${f}\left({x}\right)\:=\:\mathrm{ln}\left(\mathrm{1}+\mathrm{ln}{x}\right) \\ $$$${f}'\left({x}\right)\:=\:\frac{\frac{\mathrm{1}}{{x}}}{\mathrm{1}+\mathrm{ln}{x}} \\…