Question Number 212448 by hardmath last updated on 13/Oct/24 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\:\mathrm{x}\:+\:\frac{\mathrm{9}}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$ Answered by A5T last updated on 13/Oct/24 $${x}^{\mathrm{2}} −{x}+\mathrm{3}=\mathrm{0}\Rightarrow{x}^{\mathrm{3}}…
Question Number 212368 by Spillover last updated on 12/Oct/24 Answered by MathematicalUser2357 last updated on 13/Oct/24 $$\infty \\ $$ Commented by Ghisom last updated on…
Question Number 212361 by Ari last updated on 11/Oct/24 Commented by Ari last updated on 11/Oct/24 $${how}\:{is}\:{this}\:{equation}\:{solved}? \\ $$ Commented by Ghisom last updated on…
Question Number 212354 by RojaTaniya last updated on 11/Oct/24 $$\:\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\:{a},{b},{c}\:{and}\:{two}\:{roots}\:{of}\:{the}\:{eqn}. \\ $$$$\:{are}\:\mathrm{5}\:{consecutive}\:{integers}\:{in}\: \\ $$$$\:{some}\:{order}.\:{Find}\:{their}\:{values}. \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 212341 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\mathrm{4}\sqrt{\mathrm{2}}}{\mathrm{5}}\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\right] \\ $$$$=−\frac{\mathrm{1}}{\mathrm{20}}\underset{\mathrm{0}} {\overset{\mathrm{4}/\mathrm{5}} {\int}}\frac{{dt}}{{t}^{\mathrm{2}}…
Question Number 212326 by universe last updated on 10/Oct/24 $$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{3}\right)^{{n}} \:{n}!}{\mathrm{1}.\mathrm{4}…\left(\mathrm{3}{n}+\mathrm{1}\right)} \\ $$$$\:\left(\mathrm{1}\right)\:{check}\:\:{its}\:{a}\:{absolute}\:{conergent}\:{series} \\ $$$$\:\:\left(\mathrm{2}\right)\:{show}\:{that}\:{its}\:{a}\:{convergent}\:{series} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 212342 by hardmath last updated on 10/Oct/24 $$\mathrm{The}\:\mathrm{number}\:\:\overline {\mathrm{abc}}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{37}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\overline {\mathrm{bca}}\:+\:\overline {\mathrm{cab}}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{37}.\: \\ $$ Answered by A5T last updated on 10/Oct/24 $$\mathrm{100}{a}+\mathrm{10}{b}+{c}\equiv−\mathrm{11}{a}−\mathrm{27}{b}+{c}=−\left(\mathrm{11}{a}+\mathrm{27}{b}−{c}\right)…
Question Number 212320 by RojaTaniya last updated on 10/Oct/24 $$\:{a}+{b}+{c}+{d}=\mathrm{2},\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} =\mathrm{2} \\ $$$$\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +{d}^{\mathrm{3}} =−\mathrm{4},\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} +{d}^{\mathrm{4}} =−\mathrm{6} \\…
Question Number 212339 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{{x}^{\mathrm{3}/\mathrm{4}} \left(\mathrm{3}−{x}\right)^{\mathrm{1}/\mathrm{4}} }{\left(\mathrm{5}−{x}\right)^{\mathrm{3}} }{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\left(\frac{\mathrm{2}{x}}{\mathrm{5}\left(\mathrm{3}−{x}\right)}\right)^{\mathrm{1}/\mathrm{4}} ;\:{C}=\frac{\mathrm{9}\sqrt[{\mathrm{4}}]{\mathrm{2}}}{\mathrm{5}\sqrt[{\mathrm{4}}]{\mathrm{5}}}\right]…
Question Number 212301 by RojaTaniya last updated on 09/Oct/24 $$\:\:\:\:\mathrm{3}{x}+\frac{\mathrm{2}}{\:\sqrt{{x}}}=\mathrm{1},\:{x}−\sqrt{{x}}\:=? \\ $$$$\:\: \\ $$ Answered by Sutrisno last updated on 09/Oct/24 $${misal}\:\sqrt{{x}}={p}\rightarrow{x}={p}^{\mathrm{2}} \\ $$$$\mathrm{3}{p}^{\mathrm{2}} +\frac{\mathrm{2}}{{p}}=\mathrm{1}…