Question Number 15869 by prakash jain last updated on 14/Jun/17 $$\mathrm{If}\:{ax}^{\mathrm{2}} +\frac{{b}}{{x}}\geqslant{c}\:\mathrm{for}\:\mathrm{all}\:{x},{a},{b}>\mathrm{0}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{27}{ab}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{4}{c}^{\mathrm{2}} . \\ $$ Commented by prakash jain last…
Question Number 146943 by mathdanisur last updated on 16/Jul/21 $${b}_{\boldsymbol{{n}}+\mathrm{2}} \:\centerdot\:{b}_{\boldsymbol{{n}}+\mathrm{3}} \:\centerdot\:{b}_{\boldsymbol{{n}}+\mathrm{4}} \:=\:\mathrm{3}^{\mathrm{3}\boldsymbol{{n}}+\mathrm{3}} \\ $$$${geometric}\:{series}\:\:\boldsymbol{{b}}_{\mathrm{8}} \:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 16/Jul/21…
Question Number 146936 by mathdanisur last updated on 16/Jul/21 $$\begin{cases}{{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} +{xy}=\mathrm{37}}\\{{y}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}=\mathrm{26}}\end{cases}\:\Rightarrow\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =? \\ $$ Answered by TheHoneyCat last updated on 16/Jul/21…
Question Number 15865 by prakash jain last updated on 14/Jun/17 $${a},{b},{c}\in\mathbb{R}^{+\:} \mathrm{andIf}\:{a}+{b}+{c}=\mathrm{18}\:\mathrm{then}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{of}\:{a}^{\mathrm{2}} {b}^{\mathrm{3}} {c}^{\mathrm{4}} \:\mathrm{is} \\ $$ Answered by Tinkutara last updated on…
Question Number 146923 by mathdanisur last updated on 16/Jul/21 $${if}\:\:\:\:{arg}\:\left(\frac{{i}\:-\:{z}}{{i}}\right)\:=\:\frac{\pi}{\mathrm{4}} \\ $$$${find}\:\:\:\:{RemZ}\:+\:{ImZ}\:=\:? \\ $$ Answered by gsk2684 last updated on 16/Jul/21 $${arg}\left(\mathrm{1}+{iz}\right)=\frac{\pi}{\mathrm{4}} \\ $$$${arg}\left(\mathrm{1}+{i}\left({x}+{iy}\right)\right)=\frac{\pi}{\mathrm{4}} \\…
Question Number 146914 by mathdanisur last updated on 16/Jul/21 $$\mid{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}\mid\:=\:\mid{x}−\mathrm{4}\mid\:\Rightarrow\:{x}=? \\ $$ Answered by liberty last updated on 16/Jul/21 $$\:\mid{a}\mid=\mid{b}\mid\:\Leftrightarrow\:\left({a}+{b}\right)\left({a}−{b}\right)=\mathrm{0} \\ $$$$\Rightarrow\left({x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}+{x}−\mathrm{4}\right)\left({x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}−{x}+\mathrm{4}\right)=\mathrm{0}…
Question Number 146913 by mathdanisur last updated on 16/Jul/21 $${ax}={by}={cz}=\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:{ab}+{bc}+{ac}=\mathrm{36}{abc} \\ $$$${find}\:\:{x}+{y}+{z}=? \\ $$ Answered by liberty last updated on 16/Jul/21 $$\:\begin{cases}{{ax}=\frac{\mathrm{2}}{\mathrm{3}}}\\{{by}=\frac{\mathrm{2}}{\mathrm{3}}}\\{{cz}=\frac{\mathrm{2}}{\mathrm{3}}}\end{cases}\: \\ $$$$\Rightarrow{x}+{y}+{z}=\frac{\mathrm{2}}{\mathrm{3}}\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}\right) \\…
Question Number 81369 by mr W last updated on 12/Feb/20 Commented by mr W last updated on 12/Feb/20 $${This}\:{is}\:{a}\:{repost}\:{of}\:{Q}\mathrm{81308}. \\ $$$$ \\ $$$${I}\:{found}\:{the}\:{answer}\:{through}\:{the} \\ $$$${following}\:{way},\:{but}\:{it}\:{seems}\:{lengthy}…
Question Number 146896 by mathdanisur last updated on 16/Jul/21 $$\frac{\mathrm{5}}{\:\sqrt[{\mathrm{8}}]{\mathrm{6}}\:+\:\mathrm{1}}\:\centerdot\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{6}}\:+\:\mathrm{1}}\:\centerdot\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{6}}\:+\:\mathrm{1}}\:+\:\mathrm{1}\:=\:? \\ $$ Answered by EDWIN88 last updated on 16/Jul/21 $$\:\mathrm{What}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\frac{\mathrm{5}}{\:\sqrt[{\mathrm{8}}]{\mathrm{6}}\:+\mathrm{1}}\:×\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{6}}\:+\mathrm{1}}\:×\frac{\mathrm{1}}{\:\sqrt{\mathrm{6}}\:+\mathrm{1}}\:+\:\mathrm{1}\:. \\ $$$$\:\mathrm{Solution}\::\: \\…
Question Number 146895 by mathdanisur last updated on 16/Jul/21 $$\frac{\mathrm{1}}{\mathrm{2}\:+\:\boldsymbol{{log}}_{\mathrm{3}} \left(\mathrm{25}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{2}\:+\:\boldsymbol{{log}}_{\mathrm{5}} \left(\mathrm{9}\right)}\:=\:? \\ $$ Answered by EDWIN88 last updated on 16/Jul/21 $$\Rightarrow\:\mathrm{L}\:=\frac{\mathrm{1}}{\mathrm{2}+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{25}\right)}+\frac{\mathrm{1}}{\mathrm{2}+\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{9}\right)} \\…