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…
Question Number 204999 by Frix last updated on 05/Mar/24 $$\mathrm{Solve}\:\mathrm{for}\:{x}\in\mathbb{C} \\ $$$${x}^{\mathrm{3}} +\left(\mathrm{4}−\mathrm{3i}\right){x}^{\mathrm{2}} −\left(\mathrm{51}+\mathrm{49i}\right){x}−\mathrm{442}+\mathrm{170i}=\mathrm{0} \\ $$ Answered by Skabetix last updated on 05/Mar/24 $${S}=\left\{\:−\mathrm{9}−\mathrm{4}{i}\:;\:−\mathrm{3}+\mathrm{5}{i}\:;\:\mathrm{8}+\mathrm{2}{i}\:\right\}? \\…
Question Number 204926 by hardmath last updated on 02/Mar/24 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\bigtriangleup\mathrm{ABC} \\ $$$$\left(\mathrm{m}_{\boldsymbol{\mathrm{a}}} \:+\:\mathrm{m}_{\boldsymbol{\mathrm{b}}} \:+\:\mathrm{m}_{\boldsymbol{\mathrm{c}}} \right)^{\mathrm{2}} \:\geqslant\:\mathrm{9}\sqrt{\mathrm{3}}\:\mathrm{F} \\ $$ Commented by A5T last updated on 02/Mar/24…
Question Number 204920 by cortano12 last updated on 02/Mar/24 $$\:\:\:\:\:\mathrm{16}^{\mathrm{y}+\mathrm{x}^{\mathrm{2}} } \:+\:\mathrm{16}^{\mathrm{y}^{\mathrm{2}} +\mathrm{x}} \:=\:\mathrm{1}\: \\ $$$$\:\:\:\:\mathrm{x}+\mathrm{y}\:=? \\ $$ Answered by witcher3 last updated on 02/Mar/24…
Question Number 204916 by hardmath last updated on 01/Mar/24 $$ \\ $$How many axes of symmetry does an open angle have? Commented by mr W…