Question Number 205101 by universe last updated on 08/Mar/24 $$\:\:\mathrm{given}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{real}\:\mathrm{constant}\:\mathrm{a},\mathrm{b},\:\mathrm{c},\:\mathrm{d} \\ $$$$\:\:\mathrm{such}\:\mathrm{the}\:\mathrm{identity} \\ $$$$\:\lambda\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} =\:\left(\mathrm{ax}+\mathrm{by}\right)^{\mathrm{2}} +\left(\mathrm{cx}+\mathrm{dy}\right)^{\mathrm{2}} \:\mathrm{holds} \\ $$$$\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\mathrm{y}\:\in\:\mathbb{R}\:\mathrm{this}\:\mathrm{implies} \\ $$$$\left({a}\right)\:\lambda=−\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({b}\right)\:\lambda\geqslant\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\left({c}\right)\mathrm{0}<\lambda<\mathrm{1} \\ $$$$\:\left({d}\right)\:\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{such}\:\lambda\in\mathbb{R} \\…
Question Number 205092 by BaliramKumar last updated on 08/Mar/24 Answered by A5T last updated on 08/Mar/24 $${n}^{\mathrm{2}} +\mathrm{19}{n}+\mathrm{92}−{x}^{\mathrm{2}} =\mathrm{0} \\ $$$${n}=\frac{−\mathrm{19}\underset{−} {+}\sqrt{\mathrm{361}−\mathrm{4}\left(\mathrm{92}−{x}^{\mathrm{2}} \right)}}{\mathrm{2}}=\frac{−\mathrm{19}\underset{−} {+}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{7}}}{\mathrm{2}}…
Question Number 205107 by mnjuly1970 last updated on 08/Mar/24 $$ \\ $$$$\:\:\:\:{y}\:=\:{log}_{\mathrm{2}} \left({sin}\left({x}\right)+{cos}\left({x}\right)\right) \\ $$$$\:\:\:\Rightarrow\:\:{R}_{{y}} \:=\:?\left({Range}\:\right) \\ $$$$ \\ $$ Commented by mr W last…
Question Number 205091 by TonyCWX08 last updated on 08/Mar/24 $${f}:{z}\:\Rightarrow\:{z} \\ $$$${f}:{z}\:\Rightarrow\:{z}_{{n}} \\ $$$${f}:{z}_{{n}} \Rightarrow\:{z}_{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205083 by BaliramKumar last updated on 07/Mar/24 Answered by A5T last updated on 07/Mar/24 $$\mathrm{1}×\mathrm{1}×\mathrm{30};\mathrm{1}×\mathrm{2}×\mathrm{15};\mathrm{1}×\mathrm{3}×\mathrm{10};\mathrm{1}×\mathrm{5}×\mathrm{6}; \\ $$$$\mathrm{2}×\mathrm{3}×\mathrm{5};\:{There}\:{are}\:\mathrm{5}\:{ways}\:{upto}\:{permutation} \\ $$$${but}\:{if}\:{order}\:{matters}\:{there}\:{are},\:\mathrm{4}×\mathrm{3}!+\frac{\mathrm{3}!}{\mathrm{2}!}=\mathrm{27} \\ $$ Commented by…
Question Number 205073 by mr W last updated on 07/Mar/24 $${if}\:{a},\:{b},\:{c}\:{are}\:{the}\:{roots}\:{of} \\ $$$${f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{2024}{x}^{\mathrm{2}} +\mathrm{2024}{x}+\mathrm{2024} \\ $$$${find}\:\frac{\mathrm{1}}{\mathrm{1}−{a}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{1}−{b}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{1}−{c}^{\mathrm{2}} }=? \\ $$ Answered by cortano12…
Question Number 205053 by Abdullahrussell last updated on 06/Mar/24 Commented by Frix last updated on 08/Mar/24 $${x}=\mathrm{3} \\ $$$${y}=\frac{\mathrm{3}}{\mathrm{2}}+\frac{\sqrt{\mathrm{11}}}{\mathrm{2}}\mathrm{i} \\ $$$${z}=\frac{\mathrm{3}}{\mathrm{2}}−\frac{\sqrt{\mathrm{11}}}{\mathrm{2}}\mathrm{i} \\ $$$${x}+{y}+{z}=\mathrm{6} \\ $$…
Question Number 205021 by BaliramKumar last updated on 06/Mar/24 $${x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\mathrm{6}\:=\:\mathrm{0}\:\&\:{x}^{\mathrm{2}} \:+\:{kx}\:+\:\mathrm{1}\:=\:\mathrm{0}\:{have}\:{a}\: \\ $$$${common}\:{root}\:\mathrm{then}\:\:{k}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 06/Mar/24 $${x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\mathrm{6}\:=\:\mathrm{0}\:\&\:{x}^{\mathrm{2}}…
Question Number 205018 by BaliramKumar last updated on 06/Mar/24 $$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\:'\mathrm{k}'\:\mathrm{can}\:\mathrm{be}\:\mathrm{expression}\:{x}^{\mathrm{3}} \:+\:{kx}^{\mathrm{2}} \:−\mathrm{7}{x}\:+\mathrm{6}\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{be}\:\mathrm{resolved}\:\mathrm{into}\:\mathrm{three}\:\mathrm{linear}\:\mathrm{factors}? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{3} \\ $$ Commented by Rasheed.Sindhi last updated on 06/Mar/24…
Question Number 205051 by mr W last updated on 06/Mar/24 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{k}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{expr}{e}\mathrm{ssion}\:\mathrm{x}^{\mathrm{3}} +\:\mathrm{kx}^{\mathrm{2}} −\mathrm{7x}+\mathrm{6}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{re}{s}\mathrm{olved}\:\mathrm{into}\:\mathrm{three}\:\mathrm{linear}\:\mathrm{real}\:\mathrm{factors}. \\ $$ Answered by Frix last updated on…