Question Number 59624 by naka3546 last updated on 12/May/19 $${Rationalize}\:\:\:{the}\:\:{denominator}\:\:{of} \\ $$$$\:\:\:\:\:\:\frac{\mathrm{2}}{\:\sqrt{{x}+\mathrm{2}}\:\:+\:\:\sqrt{{x}+\mathrm{1}}\:\:+\:\:\sqrt{{x}}} \\ $$ Answered by MJS last updated on 12/May/19 $$\frac{\mathrm{1}}{\:\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}}=\frac{\sqrt{{a}}−\sqrt{{b}}−\sqrt{{c}}}{{a}−{b}−{c}−\mathrm{2}\sqrt{{bc}}}= \\ $$$$=\frac{\left(\sqrt{{a}}−\sqrt{{b}}−\sqrt{{c}}\right)\left({a}−{b}−{c}+\mathrm{2}\sqrt{{bc}}\right)}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 190686 by Yacouba last updated on 09/Apr/23 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x} \\ $$$${e}^{\mathrm{ln}\left(\mathrm{2}{x}+\mathrm{5}\right)} =\mathrm{ln}{e}\left(\mathrm{8}{x}+\mathrm{3}\right) \\ $$ Answered by aba last updated on 09/Apr/23 $$\mathrm{e}^{\mathrm{ln}\left(\mathrm{2x}+\mathrm{5}\right)} =\mathrm{ln}\left(\mathrm{e}^{\mathrm{8x}+\mathrm{3}} \right)\:\Rightarrow\:\mathrm{2x}+\mathrm{5}=\mathrm{8x}+\mathrm{3}\:\Rightarrow\:\mathrm{x}=\frac{\mathrm{1}}{\mathrm{3}}…
Question Number 190672 by 073 last updated on 08/Apr/23 Answered by aba last updated on 08/Apr/23 $$\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{e}^{\mathrm{2}} }\right)\pi? \\ $$ Commented by 073 last updated…
Question Number 59600 by Gulay last updated on 12/May/19 Answered by MJS last updated on 12/May/19 $$\left({a}+{b}\sqrt{\mathrm{3}}\right)^{\mathrm{2}} =\mathrm{14}+\mathrm{3}\sqrt{\mathrm{3}} \\ $$$${a}^{\mathrm{2}} +\mathrm{3}{b}^{\mathrm{2}} +\mathrm{2}{ab}\sqrt{\mathrm{3}}=\mathrm{14}+\mathrm{3}\sqrt{\mathrm{3}} \\ $$$$\Rightarrow \\…
Question Number 59595 by Gulay last updated on 12/May/19 Commented by Gulay last updated on 12/May/19 $$\mathrm{sir}\:\mathrm{could}\:\mathrm{you}\:\mathrm{belp}\:\mathrm{me} \\ $$ Answered by tanmay last updated on…
Question Number 190660 by vishal1234 last updated on 08/Apr/23 $${if}\:{y}\:=\:{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{where}\:{x}\in\left[−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right],\:{then}\:{find}\:\frac{{dy}}{{dx}}. \\ $$ Answered by BaliramKumar last updated on 08/Apr/23 $$\mathrm{let},\:{x}\:=\:{sin}\theta\:\Rightarrow\:\theta\:=\:{sin}^{−\mathrm{1}} {x} \\ $$$${y}\:=\:{sin}^{−\mathrm{1}}…
Question Number 190667 by 073 last updated on 08/Apr/23 Answered by manxsol last updated on 08/Apr/23 $${ABABAB}\:\mid\:{AB} \\ $$$$\underset{−} {{AB}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{10101} \\ $$$$\:\:\:\:\:\mathrm{0}{A}\boldsymbol{{B}} \\ $$$$\:\:\:\:\:\:\:\:\underset{−} {{AB}}…
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Question Number 190639 by otchereabdullai last updated on 07/Apr/23 $$\:{The}\:{points}\:{A},\:{B}\:{and}\:{C}\:{have}\:{position} \\ $$$$\:{vectors}\:{i}−{j}\:,\:\mathrm{5}{i}−\mathrm{3}{j}\:{and}\:\mathrm{11}{i}−\mathrm{6}{j}\: \\ $$$${respectively}\:.\:{Show}\:{that}\:{A},\:{B}\:{and}\:{C} \\ $$$${are}\:{collinear}. \\ $$ Answered by ajfour last updated on 08/Apr/23…
Question Number 125089 by bounhome last updated on 08/Dec/20 $${lim}_{{x}\rightarrow−\infty} \left(\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}−{x}\right)=? \\ $$ Answered by Bird last updated on 08/Dec/20 $${f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}−{x}\:\Rightarrow \\ $$$${f}\left({x}\right)=\mid{x}\mid\sqrt{\mathrm{1}+\frac{\mathrm{3}}{{x}}}−{x}…