Question Number 78503 by jagoll last updated on 18/Jan/20 $${if}\:{x},{y}\:>\mathrm{1}\: \\ $$$${prove}\:\frac{{x}^{\mathrm{2}} }{{y}−\mathrm{1}}+\frac{{y}^{\mathrm{2}} }{{x}−\mathrm{1}}\geqslant\mathrm{8} \\ $$ Answered by ~blr237~ last updated on 18/Jan/20 $$\:\mathrm{We}\:\mathrm{know}\:\mathrm{that}\:\mathrm{for}\:\mathrm{all}\:\mathrm{a},\mathrm{b}\in\mathbb{R}\: \\…
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Question Number 12962 by tawa last updated on 07/May/17 Answered by sandy_suhendra last updated on 09/May/17 Commented by sandy_suhendra last updated on 09/May/17 $$\left.\mathrm{a}\right)\:\mathrm{from}\:\mathrm{picture}\:\left(\mathrm{i}\right) \\…
Question Number 78496 by TawaTawa last updated on 18/Jan/20 Commented by mathmax by abdo last updated on 18/Jan/20 $${miss}\:{tawa}\:{are}\:{a}\:{theatcher}\:{or}\:{engineer}… \\ $$ Commented by TawaTawa last…
Question Number 144031 by mathdanisur last updated on 20/Jun/21 Answered by mindispower last updated on 20/Jun/21 $$\frac{\mathrm{1}}{{sin}\left(\mathrm{2}^{{k}} \right)}+\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}} \right)}=\frac{\mathrm{1}+{cos}\left(\mathrm{2}{k}\right)}{{sin}\left(\mathrm{2}{k}\right)}=\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}−\mathrm{1}} \right)} \\ $$$$\frac{\mathrm{1}}{{sin}\left(\mathrm{2}^{{k}} \right)}=\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}−\mathrm{1}} \right)}−\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}} \right)}…
Question Number 78493 by Rio Michael last updated on 18/Jan/20 $${the}\:{sum}\:{to}\:{infinity}\:{of}\:{a}\:{Geometric}\:{series}\:{is}\:{S} \\ $$$${the}\:{sum}\:{to}\:{infinty}\:{of}\:{the}\:{squares}\:{of}\:{the}\:{terms} \\ $$$${of}\:{the}\:{series}\:{is}\:\mathrm{2}{S} \\ $$$${the}\:{sum}\:{to}\:{infinity}\:{of}\:{the}\:{cubes}\:{of}\:{the}\:{terms} \\ $$$${of}\:{the}\:{series}\:{is}\:\frac{\mathrm{64}}{\mathrm{13}}{S}. \\ $$$${find}\:{the}\:{value}\:{of}\:{S}\:{and}\:{write}\:{iut}\:{the}\:{first} \\ $$$$\mathrm{3}\:{terms}\:{if}\:{the}\:{series}. \\ $$…
Question Number 144025 by ZiYangLee last updated on 20/Jun/21 $$\mathrm{Between}\:\mathrm{12}\:\mathrm{p}.\mathrm{m}.\:\mathrm{today}\:\mathrm{and}\:\mathrm{12}\:\mathrm{p}.\mathrm{m}. \\ $$$$\mathrm{tomorrow},\:\mathrm{how}\:\mathrm{many}\:\mathrm{times}\:\mathrm{do}\:\mathrm{the} \\ $$$$\mathrm{hour}\:\mathrm{hand}\:\mathrm{and}\:\mathrm{the}\:\mathrm{minute}\:\mathrm{hand}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{clock}\:\mathrm{form}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{120}°? \\ $$ Answered by mr W last updated on…
Question Number 78490 by ~blr237~ last updated on 18/Jan/20 $$\mathrm{Find}\:\mathrm{out}\:\mathrm{A}\:=\underset{\mathrm{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\:\frac{\zeta\left(\mathrm{n}\right)}{\mathrm{n}\left(−\mathrm{3}\right)^{\mathrm{n}} }\:\:\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\zeta\left(\mathrm{p}\right)=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{p}} }\: \\ $$ Answered by mind is power last updated…
Question Number 144026 by mohammad17 last updated on 20/Jun/21 Commented by mohammad17 last updated on 20/Jun/21 $${help}\:{me}\:{sir} \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 78489 by ~blr237~ last updated on 18/Jan/20 $$\mathrm{let}\:\:\mathrm{P}\left(\mathrm{x}\right)=\:\mathrm{x}^{\mathrm{5}} −\mathrm{209x}+\mathrm{56}\: \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{two}\:\mathrm{roots}\:\:\mathrm{a},\mathrm{b}\:\mathrm{such}\:\mathrm{as}\:\:\:\mathrm{ab}=\mathrm{1} \\ $$$$\mathrm{Find}\:\mathrm{out}\:\mathrm{their}\:\mathrm{sum}\:\left(\:\mathrm{a}+\mathrm{b}=?\right)\:\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{of}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{prime}\:\mathrm{factors}. \\ $$ Answered by MJS last updated on 18/Jan/20 $$\mathrm{2}\:\mathrm{roots}\:\mathrm{with}\:{ab}=\mathrm{1}\:\Rightarrow\:\mathrm{we}\:\mathrm{have}\:\mathrm{a}\:\mathrm{square}\:\mathrm{factor}…