Question Number 4670 by malwaan last updated on 20/Feb/16 $${prove}\:{that} \\ $$$$\mathrm{0}.\mathrm{101101110}\rightarrow\: \\ $$$${irrational}\:{number} \\ $$ Commented by prakash jain last updated on 21/Feb/16 $$\mathrm{Non}−\mathrm{recurring}\:\mathrm{non}−\mathrm{terminating}\:\mathrm{decimals}…
Question Number 4653 by FilupSmith last updated on 18/Feb/16 $$\mathrm{Silly}\:\mathrm{question} \\ $$$${which}\:{is}\:{correct}??? \\ $$$$ \\ $$$$\mathrm{ln}\left(\frac{{n}}{{ab}}\right)=\mathrm{ln}\left({n}\right)−\mathrm{ln}\left({ab}\right)=\mathrm{ln}\left({n}\right)−\mathrm{ln}\left({a}\right)+\mathrm{ln}\left({b}\right) \\ $$$${or} \\ $$$$\mathrm{ln}\left(\frac{{n}}{{ab}}\right)=\mathrm{ln}\left({n}\right)−\mathrm{ln}\left({ab}\right)=\mathrm{ln}\left({n}\right)−\mathrm{ln}\left({a}\right)−\mathrm{ln}\left({b}\right) \\ $$ Answered by 123456…
Question Number 4630 by sanusihammed last updated on 15/Feb/16 $${Solve}\:{for}\:{x}\:{in}\:{the}\:{equation} \\ $$$$\mathrm{4}^{{x}\:} =\:\mathrm{8}{x} \\ $$$$ \\ $$$${I}\:{know}\:{the}\:{answer}\:{is}\:\mathrm{2}.\:{I}\:{need}\:{the}\:{solution}.\:{Thanks} \\ $$$$ \\ $$ Commented by FilupSmith last…
Question Number 70162 by TawaTawa last updated on 01/Oct/19 Answered by mind is power last updated on 01/Oct/19 $$\Rightarrow\mathrm{1}=\left({a}+{b}\right)\left(\frac{{sin}^{\mathrm{4}} \left(\theta\right)}{{a}}+\frac{{cos}^{\mathrm{4}} \left(\theta\right)}{{b}}\right)…{S} \\ $$$$\Rightarrow\frac{{b}}{{a}}{Sin}^{\mathrm{4}} \left(\theta\right)+\frac{{a}}{{b}}{cos}^{\mathrm{4}} \left(\theta\right)+{cos}^{\mathrm{4}}…
Question Number 70161 by TawaTawa last updated on 01/Oct/19 Answered by mind is power last updated on 01/Oct/19 $${let}\:{a}=\sqrt{\sqrt{\mathrm{5}}+\mathrm{2}}\:\:{b}=\sqrt{\sqrt{\mathrm{5}}−\mathrm{2}} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{2}\sqrt{\mathrm{5}} \\ $$$${ab}=\mathrm{1}…
Question Number 4622 by sanusihammed last updated on 14/Feb/16 $${what}\:{is}\:{the}\:{value}\:{of}\:{x}\:{in}\: \\ $$$$\mathrm{2}{x}\:+\:\mathrm{5}\:=\:\mathrm{10} \\ $$ Answered by sanusihammed last updated on 14/Feb/16 $${collect}\:{the}\:{like}\:{terms} \\ $$$$\mathrm{2}{x}\:=\:\mathrm{10}\:−\:\mathrm{5} \\…
Question Number 135682 by liberty last updated on 15/Mar/21 $$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}^{\mathrm{3}} +\mathrm{2}{k}}{{k}^{\mathrm{2}} +\mathrm{6}{k}+\mathrm{9}}\:=? \\ $$ Answered by abdullahoudou last updated on 15/Mar/21 $$\infty \\…
Question Number 70135 by petrochengula last updated on 01/Oct/19 $${sophie}−{Germain}\:{identity} \\ $$$${a}^{\mathrm{4}} +\mathrm{4}{b}^{\mathrm{4}} =\left(\left({a}+{b}\right)^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\left(\left({a}−{b}\right)^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$ Commented by mathmax by abdo…
Question Number 4582 by FilupSmith last updated on 08/Feb/16 $${S}=\mathrm{log}_{{a}} {i} \\ $$$${i}^{\mathrm{2}} =−\mathrm{1} \\ $$$${a}\in\mathbb{R} \\ $$$${Solve}\:{S} \\ $$$$ \\ $$$${extra}: \\ $$$$\mathrm{what}\:\mathrm{if}\:\:{a}\in\mathbb{C}? \\…
Question Number 70103 by Shamim last updated on 01/Oct/19 $$\mathrm{if}\:\mathrm{m}^{\mathrm{3}} +\mathrm{2p}^{\mathrm{3}} =\mathrm{3mn},\:\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} =\mathrm{p}^{\mathrm{3}} \:\mathrm{and} \\ $$$$\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{n}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{a}+\mathrm{b}=\mathrm{m}. \\ $$ Answered by mind is…