Question Number 13327 by Nayon last updated on 18/May/17 $${how}\:{can}\:{we}\:{expand}\:\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} ?? \\ $$ Answered by prakash jain last updated on 19/May/17 $$\left(\mathrm{1}+{x}\right)^{{y}} =\mathrm{1}+{yx}+\frac{{y}\left({y}−\mathrm{1}\right)}{\mathrm{2}!}{x}^{\mathrm{2}} +\frac{{y}\left({y}−\mathrm{1}\right)\left({y}−\mathrm{2}\right)}{\mathrm{3}!}{x}^{\mathrm{3}} +…
Question Number 78857 by mr W last updated on 21/Jan/20 $${with}\:{a},{b}\in{R}\:{prove}\:{that} \\ $$$$\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}}{bi}}+\sqrt[{\mathrm{3}}]{{a}−\sqrt{\mathrm{3}}{bi}} \\ $$$${has}\:{always}\:{real}\:{value}\:{and}\:{find}\:{this} \\ $$$${value}\:\left({or}\:{a}\:{way}\:{how}\:{to}\:{find}\right). \\ $$$${examples}: \\ $$$${a}=\mathrm{15},\:{b}=\frac{\mathrm{28}}{\mathrm{9}}\:\:\Rightarrow\:{result}=\mathrm{5} \\ $$$${a}=\mathrm{6},\:{b}=\frac{\mathrm{35}}{\mathrm{9}}\:\:\Rightarrow\:{result}=\mathrm{4} \\ $$$${a}=−\mathrm{24},\:{b}=\frac{\mathrm{80}}{\mathrm{9}}\:\:\Rightarrow\:{result}=\mathrm{4}…
Question Number 13294 by Tinkutara last updated on 17/May/17 $$\mathrm{If}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{and}\:{a}\:+\:{b}\:+\:{c}\:=\:\mathrm{2},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:+\:\mathrm{2}{abc}\:<\:\mathrm{2} \\ $$ Commented by prakash jain last updated…
Question Number 13295 by Tinkutara last updated on 17/May/17 $$\mathrm{For}\:{n}\:\in\:\mathbb{N},\:{n}\:>\:\mathrm{1},\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{n}}\:+\:\frac{\mathrm{1}}{{n}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{{n}\:+\:\mathrm{2}}\:+\:…\:+\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:>\:\mathrm{1} \\ $$ Commented by prakash jain last updated on 17/May/17 $${n}=\mathrm{2}\:{and}\:\mathrm{3}\:{can}\:{be}\:{checked} \\…
Question Number 78820 by mathocean1 last updated on 20/Jan/20 $$\mathrm{please}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{fomula}\:\mathrm{to}\: \\ $$$$\mathrm{determinate}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\: \\ $$$$\mathrm{bissectors}\:\mathrm{in}\:\mathrm{triangle}? \\ $$ Answered by MJS last updated on 21/Jan/20 $$\mathrm{bisector}\:\mathrm{between}\:\mathrm{2}\:\mathrm{lines} \\…
Question Number 144359 by mathdanisur last updated on 24/Jun/21 $$\int\:\frac{{x}^{\mathrm{4}} {e}^{{x}} \:{dx}}{\left({x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{12}{x}^{\mathrm{2}} +\mathrm{24}{x}+\mathrm{24}+\mathrm{72}{e}^{{x}} \right)^{\mathrm{2}} }\:=\:? \\ $$ Answered by mitica last updated on…
Question Number 78814 by M±th+et£s last updated on 20/Jan/20 Commented by mind is power last updated on 21/Jan/20 $$\mathrm{2}{nd}\:{Way} \\ $$$$\alpha^{\mathrm{2}} \beta^{\mathrm{2}} \gamma^{\mathrm{2}} \delta^{\mathrm{2}} +\alpha^{\mathrm{2}}…
Question Number 144340 by santoshachary1985 last updated on 24/Jun/21 $$ \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{2ab}−\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{2ab}−\mathrm{3}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{2ab}−\mathrm{3}=\mathrm{0} \\ $$$$\:\mathrm{3} \\ $$…
Question Number 144334 by mathdanisur last updated on 24/Jun/21 $${Reduct}\:{it}:\:\:\frac{\boldsymbol{{z}}^{\mathrm{8}} \:+\:\boldsymbol{{z}}\:+\:\mathrm{1}}{\boldsymbol{{z}}^{\mathrm{5}} \:+\:\boldsymbol{{z}}\:+\:\mathrm{1}} \\ $$ Answered by Olaf_Thorendsen last updated on 24/Jun/21 $$\mathrm{Z}\:=\:\frac{{z}^{\mathrm{8}} +{z}+\mathrm{1}}{{z}^{\mathrm{5}} +{z}+\mathrm{1}} \\…
Question Number 144300 by mathdanisur last updated on 24/Jun/21 Answered by Rasheed.Sindhi last updated on 25/Jun/21 $$\left({x}+\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} −{a}^{\mathrm{2}{n}+\mathrm{1}} ={x}\left({x}+\mathrm{1}\right){Q}\left({x}\right)+{ux}+{v} \\ $$$${For}\:{x}\in\mathbb{Z} \\ $$$${For}\:{x}=\mathrm{0} \\ $$$$\mathrm{1}−{a}^{\mathrm{2}{n}+\mathrm{1}}…