Question Number 13349 by tawa tawa last updated on 19/May/17 Answered by ajfour last updated on 19/May/17 $${for}\:{x}\neq\frac{\mathrm{2}}{{a}}\:,{we}\:{have} \\ $$$$\mathrm{24}{x}^{\mathrm{2}} +\mathrm{25}{x}−\mathrm{47}=−\left({ax}−\mathrm{2}\right)\left(\mathrm{8}{x}+\mathrm{3}\right)−\mathrm{53} \\ $$$$\mathrm{24}{x}^{\mathrm{2}} +\mathrm{25}{x}−\mathrm{47}=−\mathrm{8}{ax}^{\mathrm{2}} +\left(\mathrm{16}−\mathrm{3}{a}\right){x}+\mathrm{6}−\mathrm{53}…
Question Number 13345 by tawa tawa last updated on 19/May/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78877 by M±th+et£s last updated on 21/Jan/20 $${if}\:\:\:\frac{{sin}\left({A}\right)}{{sin}\left({B}\right)}=\frac{{sin}\left({D}\right)}{{sin}\left({C}\right)} \\ $$$${and}\:{A}+{B}={C}+{D} \\ $$$$ \\ $$$${then}\:{prove}\:{that}\:\: \\ $$$${A}+{B}=\mathrm{180} \\ $$$${C}+{D}=\mathrm{180} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Commented…
Question Number 144408 by mathdanisur last updated on 25/Jun/21 $$\boldsymbol{{lg}}\left(\mathrm{2}\right)=\boldsymbol{{x}} \\ $$$$\boldsymbol{{lg}}\left(\mathrm{7}\right)=\boldsymbol{{y}} \\ $$$$\boldsymbol{{lg}}_{\mathrm{5}} \left(\mathrm{9},\mathrm{8}\right)=? \\ $$ Answered by liberty last updated on 25/Jun/21 $$\:\begin{cases}{\mathrm{log}\:_{\mathrm{10}}…
Question Number 13333 by mrW1 last updated on 19/May/17 $${About}\:{the}\:{solution}\:{to}\:{question}: \\ $$$${For}\:{a},{b},{c}>\mathrm{0}\:{and}\:{abc}=\mathrm{1},\:{prove} \\ $$$${a}^{{b}+{c}} {b}^{{c}+{a}} {c}^{{a}+{b}} \leqslant\mathrm{1} \\ $$$$ \\ $$$${Way}\:\mathrm{1}: \\ $$$${Let}'{s}\:{say}\:{a}\leqslant{b}\leqslant{c}. \\ $$$${We}\:{can}\:{prove}\:{that}\:{a}\leqslant\mathrm{1}:…
Question Number 13328 by Nayon last updated on 18/May/17 $${Can}\:{we}\:{define}\:{factorial}\:{for}\:{any}\: \\ $$$${real}\:{number}??? \\ $$ Answered by prakash jain last updated on 18/May/17 $${x}!=\Gamma\left({x}+\mathrm{1}\right),\:{x}\in\mathbb{R} \\ $$$$…
Question Number 13327 by Nayon last updated on 18/May/17 $${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} \\…