Question Number 137208 by bemath last updated on 31/Mar/21 $$\mathrm{If}\:\mathrm{x},\mathrm{y}\:>\:\mathrm{0}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\:\mathrm{3}\sqrt{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\:+\:\sqrt{\mathrm{xy}}\:\geqslant\:\mathrm{2}\left(\mathrm{x}+\mathrm{y}\right)\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 71674 by TawaTawa last updated on 18/Oct/19 Answered by mind is power last updated on 18/Oct/19 $$\mathrm{what}\:\mathrm{de}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by}\:\mathrm{n}^{\mathrm{n}^{\mathrm{n}^{\mathrm{n}^{\mathrm{0}} } } } ? \\ $$$$…
Question Number 137209 by JulioCesar last updated on 31/Mar/21 Answered by bemath last updated on 31/Mar/21 $$\int\:\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \mathrm{sec}\:\mathrm{x}\:\mathrm{dx} \\ $$$$=\int\left(\mathrm{sec}\:^{\mathrm{5}} \mathrm{x}−\mathrm{2sec}\:^{\mathrm{3}} \mathrm{x}+\mathrm{sec}\:\mathrm{x}\:\right)\mathrm{dx} \\ $$$$\mathrm{now}\:\mathrm{it}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{solve}…
Question Number 71666 by aliesam last updated on 18/Oct/19 $${f}:{z}\rightarrow{z} \\ $$$$ \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{3}\left(\mathrm{4}{xy}−\mathrm{1}\right) \\ $$$$ \\ $$$$,{f}\left(\mathrm{1}\right)=\mathrm{0} \\ $$$$ \\ $$$$\forall{x},{y}\:\in{z} \\ $$$${evaluate}\:{f}\left(\mathrm{19}\right) \\…
Question Number 6115 by Rasheed Soomro last updated on 14/Jun/16 $${Solve}\:{the}\:{system}\:{of}\:{following}\:{equations} \\ $$$${a}^{\mathrm{3}} −{bcd}=−\mathrm{32} \\ $$$${b}^{\mathrm{3}} −{acd}=−\mathrm{79} \\ $$$${c}^{\mathrm{3}} −{abd}=\mathrm{109} \\ $$$${d}^{\mathrm{3}} −{abc}=\mathrm{502} \\ $$…
Question Number 137173 by JulioCesar last updated on 30/Mar/21 Commented by mathmax by abdo last updated on 31/Mar/21 $$\mathrm{not}\:\mathrm{defined}\:\:\:\mathrm{arcsin}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{on}\:\left[−\mathrm{1},\mathrm{1}\right]\:\:\mathrm{but}\:\mathrm{x}^{\mathrm{2}} −\mathrm{1}\leqslant\mathrm{0}\:! \\ $$ Answered by Ñï=…
Question Number 6105 by sanusihammed last updated on 13/Jun/16 $${Solve}\:{the}\:{system}\:{of}\:{equation}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} \:−\:{yz}\:=\:−\:\mathrm{52}\:\:\:…………..\:\left({i}\right) \\ $$$${y}^{\mathrm{2}} \:−\:{xz}\:=\:−\:\mathrm{6}\:…………….\:\left({ii}\right) \\ $$$${z}^{\mathrm{2}} \:−\:{xy}\:=\:\mathrm{86}\:\:\:…………..\:\left({iii}\right) \\ $$ Commented by…
Question Number 71633 by mind is power last updated on 18/Oct/19 $$\mathrm{let}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\in\mathrm{IR}_{+} \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}+\mathrm{c}\right)\geqslant\mathrm{2}\sqrt{\mathrm{abc}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)} \\ $$$$ \\ $$ Answered by MJS last updated on 18/Oct/19…
Question Number 137117 by MathZa last updated on 29/Mar/21 Answered by mathmax by abdo last updated on 30/Mar/21 $$\mathrm{is}\:\mathrm{z}+\mathrm{i}\sqrt{\mathrm{2}}=\mathrm{0}? \\ $$$$\mathrm{z}+\mathrm{i}\sqrt{\mathrm{2}}=\frac{\mathrm{2}−\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}}\mathrm{i}}{\mathrm{1}+\sqrt{\mathrm{2}}\mathrm{i}−\mathrm{i}}\:+\sqrt{\mathrm{2}}\mathrm{i}\:=\frac{\mathrm{2}−\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}}\mathrm{i}+\sqrt{\mathrm{2}}\mathrm{i}−\mathrm{2}+\sqrt{\mathrm{2}}}{\mathrm{1}+\sqrt{\mathrm{2}}\mathrm{i}\:−\mathrm{i}} \\ $$$$=\frac{\mathrm{2}\sqrt{\mathrm{2}}\mathrm{i}}{\mathrm{1}+\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\mathrm{i}}\:=\frac{\mathrm{2}\sqrt{\mathrm{2}}\mathrm{i}\left(\mathrm{1}−\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\mathrm{i}\right.}{\mathrm{1}+\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} }\:=\frac{\mathrm{2}\sqrt{\mathrm{2}}\mathrm{i}+\mathrm{2}\sqrt{\mathrm{2}}\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)}{\mathrm{1}+\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} }…
Question Number 6045 by sanusihammed last updated on 10/Jun/16 $$\mathrm{4}^{{x}} \:=\:\mathrm{2}{x} \\ $$$$ \\ $$$${find}\:{x} \\ $$ Commented by Yozzii last updated on 10/Jun/16 $$\mathrm{4}^{{x}}…