Question Number 188069 by mustafazaheen last updated on 25/Feb/23 $${how}\:{is}\:{solution} \\ $$$$\int\sqrt{{e}^{{x}} }\mathrm{ln}\:\sqrt{{e}^{{x}} }{dx}=? \\ $$ Commented by 0670322918 last updated on 25/Feb/23 Terms of…
Question Number 56991 by Tawa1 last updated on 28/Mar/19 $$\:\:\mathrm{x}!\:−\:\mathrm{x}^{\mathrm{2}} \:\:=\:\:\mathrm{8}\:,\:\:\:\:\mathrm{Find}\:\:\mathrm{x} \\ $$$$ \\ $$ Commented by Joel578 last updated on 28/Mar/19 $${x}\:=\:\mathrm{4} \\ $$…
Question Number 122523 by greg_ed last updated on 17/Nov/20 Answered by 676597498 last updated on 17/Nov/20 $${A}=\frac{{x}+{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{x}}=\frac{{x}\left(\mathrm{1}+{x}\right)}{{x}\left({x}−\mathrm{1}\right)}=\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\:\forall{x}\geqslant\mathrm{0} \\ $$$${or} \\ $$$${A}=\frac{−{x}+{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} −−{x}}=\frac{{x}\left({x}−\mathrm{1}\right)}{{x}\left({x}+\mathrm{1}\right)}=\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\:\forall{x}<\mathrm{0}…
Question Number 188016 by Rupesh123 last updated on 24/Feb/23 Answered by aleks041103 last updated on 24/Feb/23 $${f}=\left({x}^{\mathrm{3}} +{y}^{\mathrm{2}} \right)^{\mathrm{1}/\mathrm{2}} \\ $$$${df}=\frac{\partial{f}}{\partial{x}}{dx}+\frac{\partial{f}}{\partial{y}}{dy}= \\ $$$$=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}\sqrt{{x}^{\mathrm{3}} +{y}^{\mathrm{2}}…
Question Number 187998 by Mingma last updated on 24/Feb/23 Answered by mahdipoor last updated on 24/Feb/23 $$=\frac{\left(\mathrm{16}−\mathrm{2}\right)\left(\mathrm{16}+\mathrm{2}\right)}{\mathrm{18}×\mathrm{13}}×\frac{\left(\mathrm{16}−\mathrm{3}\right)\left(\mathrm{16}+\mathrm{3}\right)}{\mathrm{19}×\mathrm{12}}×…×\frac{\left(\mathrm{16}−\mathrm{8}\right)\left(\mathrm{16}+\mathrm{8}\right)}{\mathrm{24}×\mathrm{7}} \\ $$$$=\frac{\mathrm{14}}{\mathrm{13}}×\frac{\mathrm{13}}{\mathrm{12}}×…×\frac{\mathrm{8}}{\mathrm{7}}=\frac{\mathrm{14}}{\mathrm{7}}=\mathrm{2} \\ $$ Commented by Mingma last…
Question Number 187989 by mnjuly1970 last updated on 24/Feb/23 Answered by HeferH last updated on 24/Feb/23 $$\:{b}^{\mathrm{2}} ={ac} \\ $$$$\:{b}^{\mathrm{3}} ={abc} \\ $$$$\:\frac{{b}^{\mathrm{3}} {c}^{\mathrm{3}} +{a}^{\mathrm{3}}…
Question Number 187980 by Mingma last updated on 24/Feb/23 Answered by Rasheed.Sindhi last updated on 24/Feb/23 $$\bullet{x}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}\: \\ $$$$\alpha+\beta=−{b}\:,\:\:\:\alpha\beta={c} \\ $$$$\bullet{x}^{\mathrm{2}} +{bx}−{c}=\mathrm{0} \\ $$$$\gamma+\delta=−{b}\:\:,\:\:\gamma\delta=−{c}…
Question Number 122445 by benjo_mathlover last updated on 17/Nov/20 Answered by TANMAY PANACEA last updated on 17/Nov/20 $${using}\:{Titu}\:{lemma} \\ $$$$\frac{\mathrm{1}^{\mathrm{2}} }{{x}}+\frac{\mathrm{3}^{\mathrm{2}} }{{y}}+\frac{\mathrm{5}^{\mathrm{2}} }{{z}}\geqslant\frac{\left(\mathrm{1}+\mathrm{3}+\mathrm{5}\right)^{\mathrm{2}} }{{x}+{y}+{z}} \\…
Question Number 56904 by pete last updated on 26/Mar/19 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{3x}^{\mathrm{2}} −\mathrm{x}−\mathrm{3}=\mathrm{0},\:\mathrm{find}\:\mathrm{thevalue}\:\mathrm{of}\:\left(\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} \right) \\ $$$$\mathrm{if}\:\alpha>\beta. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 187971 by mnjuly1970 last updated on 24/Feb/23 $$ \\ $$$$\:\:\mathrm{If}\:\:\:,\:\:{x}^{\:\mathrm{5}} \:=\:\mathrm{1}\:\:\:\wedge\:\:{x}\neq\mathrm{1} \\ $$$$ \\ $$$$\:\:\:\:\left(\:\frac{\:\mathrm{1}}{{x}^{\:\mathrm{2}} \:−{x}\:+\mathrm{1}}\:+\:\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} \:+\:{x}\:+\mathrm{1}}\:\right)^{\:\mathrm{10}} =\:? \\ $$$$ \\ $$ Answered…