Question Number 198954 by ArifinTanjung last updated on 26/Oct/23 $$\:\mathrm{Convert}\:\mathrm{this}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{to}\: \\ $$$$\:\:\mathrm{praction}\:\mathrm{number} \\ $$$$\mathrm{1}.\:\mathrm{0}.\mathrm{3333}…\:=… \\ $$$$\mathrm{2}.\:\:\mathrm{2}.\mathrm{1111}…=… \\ $$$$\mathrm{3}.\:\mathrm{0}.\mathrm{1313}….=… \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 199015 by Tawa11 last updated on 26/Oct/23 Answered by Rasheed.Sindhi last updated on 26/Oct/23 $$\sqrt{{a}−{x}}\:+\sqrt{{b}−{x}}\:+\sqrt{{c}−{x}}\:=\mathrm{0} \\ $$$$\sqrt{{a}−{x}}\:=\mathrm{0}\:\wedge\:\sqrt{{b}−{x}}\:=\mathrm{0}\:\wedge\:\sqrt{{c}−{x}}\:=\mathrm{0} \\ $$$${x}={a}={b}={c} \\ $$$$\left({a}+{b}+{c}+\mathrm{3}{x}\right)\left({a}+{b}+{c}−{x}\right)=\mathrm{4}\left({bc}+{ca}+{ab}\right) \\ $$$$\left({x}+{x}+{x}+\mathrm{3}{x}\right)\left({x}+{x}+{x}−{x}\right)=\mathrm{4}\left({x}.{x}+{x}.{x}+{x}.{x}\right)…
Question Number 198951 by ArifinTanjung last updated on 26/Oct/23 $$\sqrt{\mathrm{8}+\sqrt{\mathrm{48}}\:}=….? \\ $$ Commented by mr W last updated on 26/Oct/23 $${are}\:{you}\:{serious}? \\ $$$${you}\:{ask}\:{both}\:{this}\:\sqrt{\mathrm{8}+\sqrt{\mathrm{48}}\:}=…. \\ $$$${and}\:{this}\:\int_{\mathrm{1}}…
Question Number 198902 by necx122 last updated on 25/Oct/23 $${Given}\:{that}\:{k}^{\mathrm{2}} −\mathrm{3}{k}+\mathrm{5}=\mathrm{0},\:{determine} \\ $$$${the}\:{value}\:{of}\:{k}^{\mathrm{4}} −\mathrm{6}{k}^{\mathrm{3}} +\mathrm{9}{k}^{\mathrm{2}} −\mathrm{7} \\ $$ Answered by witcher3 last updated on 25/Oct/23…
Question Number 198903 by necx122 last updated on 25/Oct/23 $${Find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\frac{{a}}{{b}+{c}}+\frac{{b}}{{c}+{a}}+\frac{{c}}{{a}+{b}}\:{for}\:{all}\:{positive}\:{real} \\ $$$${numbers} \\ $$ Commented by necx122 last updated on 25/Oct/23 please I need help with this Answered…
Question Number 198932 by necx122 last updated on 25/Oct/23 $${Find}\:{the}\:{value}\:{of}\:{m}\:{given}\:{that}\:{the} \\ $$$${roots}\:{of}\:{x}^{\mathrm{4}} −\mathrm{15}{x}^{\mathrm{3}} +\mathrm{70}{x}^{\mathrm{2}} −\mathrm{120}{x}+{m}=\mathrm{0} \\ $$$${form}\:{a}\:{geometric}\:{progression}. \\ $$ Answered by AST last updated on…
Question Number 198931 by necx122 last updated on 25/Oct/23 $${Find}\:{the}\:{value}\:{of}\:{t}:\: \\ $$$${t}\:=\:\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{9}}+\frac{\mathrm{3}}{\mathrm{27}}+…….+\frac{{n}}{\mathrm{3}^{{n}} }+….. \\ $$ Answered by cortano12 last updated on 26/Oct/23 $$\:\mathrm{t}=\frac{\mathrm{1}}{\mathrm{3}}\:+\frac{\mathrm{2}}{\mathrm{9}}\:+\frac{\mathrm{3}}{\mathrm{27}}\:+\ldots+\:\frac{\mathrm{n}}{\mathrm{3}^{\mathrm{n}} }\: \\…
Question Number 198919 by necx122 last updated on 25/Oct/23 $${Find}\:{the}\:{sum}\:{of}\:{the}\:{fourth}\:{powers}\:{of} \\ $$$${the}\:{roots}\:{of}\:{equation}: \\ $$$$\mathrm{7}{x}^{\mathrm{3}} −\mathrm{21}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{2}=\mathrm{0} \\ $$ Commented by necx122 last updated on 25/Oct/23…
Question Number 198850 by mustafazaheen last updated on 25/Oct/23 $$ \\ $$$$\mathrm{p}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{p}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{4x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=? \\ $$$$ \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last…
Question Number 198814 by hardmath last updated on 24/Oct/23 $$\mathrm{Simplify}: \\ $$$$\frac{\left(\sqrt{\mathrm{x}\:+\:\mathrm{4}\:\sqrt{\mathrm{x}\:-\:\mathrm{4}}}\:+\:\sqrt{\mathrm{x}\:-\:\mathrm{4}\:\sqrt{\mathrm{x}\:-\:\mathrm{4}}}\right)\:\sqrt{\mathrm{x}\:-\:\mathrm{8}}}{\mathrm{4}\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{12x}\:+\:\mathrm{32}}} \\ $$ Answered by a.lgnaoui last updated on 24/Oct/23 $$=\frac{\mathrm{1}}{\mathrm{4}}\sqrt{\frac{\mathrm{x}+\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}{\boldsymbol{\mathrm{x}}−\mathrm{4}}}\:+\frac{\mathrm{1}}{\mathrm{4}}\sqrt{\frac{\boldsymbol{\mathrm{x}}−\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}{\boldsymbol{\mathrm{x}}−\mathrm{4}}} \\ $$$$=\frac{\sqrt{\boldsymbol{\mathrm{x}}+\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}\:}\:+\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}}{\:\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}…