Question Number 189624 by Rupesh123 last updated on 19/Mar/23 Answered by Rasheed.Sindhi last updated on 19/Mar/23 $${x}^{\mathrm{2}} −\left({a}+{b}\right){x}+{ab}={x}^{\mathrm{2}} +\left({c}−\mathrm{6}\right){x}−\mathrm{6}{c}+\mathrm{5} \\ $$$$−\left({a}+{b}\right)={c}−\mathrm{6}\:\:\wedge\:{ab}=\mathrm{5}−\mathrm{6}{c} \\ $$$${c}=−{a}−{b}+\mathrm{6}\:\wedge\:{ab}=\mathrm{5}−\mathrm{6}\left(−{a}−{b}+\mathrm{6}\right) \\ $$$${ab}=\mathrm{6}{a}+\mathrm{6}{b}−\mathrm{31}…
Question Number 189625 by Rupesh123 last updated on 19/Mar/23 Commented by Rupesh123 last updated on 19/Mar/23 Can you explain? Answered by Frix last updated on 19/Mar/23 $$…,{n}−\mathrm{1},{n},{n},{n},{n},{n},{n},{n},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{2},……
Question Number 189563 by Rupesh123 last updated on 18/Mar/23 Answered by FelipeLz last updated on 19/Mar/23 $${V}\:=\:\left({r}_{\mathrm{1}} +\mathrm{2}\right)×\left({r}_{\mathrm{2}} +\mathrm{2}\right)×\left({r}_{\mathrm{3}} +\mathrm{2}\right)\:=\:{r}_{\mathrm{1}} {r}_{\mathrm{2}} {r}_{\mathrm{3}} +\mathrm{2}\left({r}_{\mathrm{1}} {r}_{\mathrm{2}} +{r}_{\mathrm{1}}…
Question Number 189506 by Rupesh123 last updated on 18/Mar/23 Answered by HeferH last updated on 18/Mar/23 Commented by HeferH last updated on 18/Mar/23 $$\mathrm{Area}\:=\:\mathrm{12}×\mathrm{14}\:−\:\left(\frac{\mathrm{12}×\mathrm{7}+\mathrm{7}×\mathrm{6}+\mathrm{14}×\mathrm{6}}{\mathrm{2}}\right) \\…
Question Number 189464 by Rupesh123 last updated on 17/Mar/23 Answered by Rasheed.Sindhi last updated on 17/Mar/23 $$\mathrm{4}{a}_{{n}+\mathrm{1}} ^{\mathrm{2}} −\mathrm{4}{a}_{{n}} {a}_{{n}+\mathrm{1}} +{a}_{{n}} ^{\mathrm{2}} −\mathrm{1}=\mathrm{0} \\ $$$${n}=\mathrm{1}:…
Question Number 58362 by peter frank last updated on 22/Apr/19 $$\int\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:\mathrm{3}{x}}{dx} \\ $$ Answered by mr W last updated on 22/Apr/19 $$=\int\frac{\mathrm{sin}\:{x}}{\mathrm{3}\:\mathrm{sin}\:{x}−\mathrm{4}\:\mathrm{sin}^{\mathrm{3}} \:{x}}\:{dx} \\ $$$$=\int\frac{\mathrm{1}}{\mathrm{3}−\mathrm{4}\:\mathrm{sin}^{\mathrm{2}}…
Question Number 123869 by benjo_mathlover last updated on 28/Nov/20 Answered by liberty last updated on 29/Nov/20 $${let}\::{a}\:,{ar},{ar}^{\mathrm{2}} ,{ar}^{\mathrm{3}} \:{the}\:{four}\:{consecutive}\:{terms}\:{in}\:{GP} \\ $$$${given}\:{the}\:{condition}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}{u}_{{i}} \:=\:{a}+{ar}+{ar}^{\mathrm{2}} +{ar}^{\mathrm{3}}…
Question Number 189357 by BaliramKumar last updated on 15/Mar/23 $$ \\ $$How many pairs of positive integers x, y exist such that HCF (x, y)…
Question Number 189267 by Rupesh123 last updated on 14/Mar/23 Commented by Rupesh123 last updated on 14/Mar/23 Find the 5-digit number ABCDE such that Answered by HeferH last updated on 14/Mar/23 $$\:\bullet\:\mathrm{E}\:=\:\mathrm{7}…
Question Number 189126 by Mingma last updated on 12/Mar/23 Answered by mr W last updated on 12/Mar/23 $${if}\:\mathrm{6}{k}\leqslant{n}<\mathrm{6}{k}+\mathrm{2}: \\ $$$$\mathrm{3}{k}+\mathrm{2}{k}+{k}={n}\:\Rightarrow{n}=\mathrm{6}{k}\:\checkmark \\ $$$${if}\:\mathrm{6}{k}+\mathrm{2}\leqslant{n}<\mathrm{6}{k}+\mathrm{3}: \\ $$$$\mathrm{3}{k}+\mathrm{1}+\mathrm{2}{k}+{k}={n}\:\Rightarrow{n}=\mathrm{6}{k}+\mathrm{1}\:\rightarrow{bad} \\…