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Category: Algebra

if-x-y-2-xy-1-5-2-and-x-2-y-2-5-find-1-x-1-y-

Question Number 153128 by mathdanisur last updated on 04/Sep/21 $$\mathrm{if}\:\:\:\frac{\mathrm{x}+\mathrm{y}}{\mathrm{2}}\:+\:\sqrt{\mathrm{xy}}\:=\:\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\sqrt{\mathrm{5}} \\ $$$$\mathrm{find}\:\:\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:=\:? \\ $$ Answered by EDWIN88 last updated on 05/Sep/21 $$\:\:\begin{cases}{{x}+{y}={u}}\\{{xy}={v}}\end{cases}\Rightarrow\begin{cases}{{u}+\mathrm{2}\sqrt{{v}}\:=\mathrm{1}+\sqrt{\mathrm{5}}}\\{{u}^{\mathrm{2}} −\mathrm{2}{v}=\sqrt{\mathrm{5}}}\end{cases}…

If-x-gt-0-and-the-4-th-term-in-the-expansion-of-2-3-8-x-10-has-maximum-value-then-find-the-range-of-x-

Question Number 22047 by Tinkutara last updated on 10/Oct/17 $$\mathrm{If}\:{x}\:>\:\mathrm{0}\:\mathrm{and}\:\mathrm{the}\:\mathrm{4}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{2}\:+\:\frac{\mathrm{3}}{\mathrm{8}}{x}\right)^{\mathrm{10}} \:\mathrm{has}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}. \\ $$ Commented by Tinkutara last updated on 10/Oct/17…

1-2-3-1-4-5-6-1-7-8-9-

Question Number 153103 by amin96 last updated on 04/Sep/21 $$\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}\centerdot\mathrm{5}\centerdot\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{7}\centerdot\mathrm{8}\centerdot\mathrm{9}}+\ldots \\ $$ Answered by puissant last updated on 04/Sep/21 $${S}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)\left(\mathrm{3}{n}+\mathrm{3}\right)} \\ $$$$=\underset{{n}=\mathrm{0}} {\overset{\infty}…

Question-87553

Question Number 87553 by TawaTawa1 last updated on 05/Apr/20 Answered by ajfour last updated on 05/Apr/20 $${let}\:{no}.\:{of}\:{boys}\:{in}\:{A}=\mathrm{3}{k} \\ $$$$\:\:\:\:………..{girls}\:\:….\:{A}\:=\:\mathrm{2}{k} \\ $$$${let}\:\:{no}.\:{of}\:{girls}\:{in}\:{B}=\:{x} \\ $$$$\&\:\:\:{no}.\:{of}\:{boys}\:{in}\:{B}\:=\:{y} \\ $$$${no}.\:{of}\:{girls}\:{in}\:{C}\:=\:{z}…

Solve-the-equation-1-z-2z-2-1-2z-1-z-2-

Question Number 153079 by mathdanisur last updated on 04/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\sqrt{\mathrm{1}-\boldsymbol{{z}}}\:=\:\mathrm{2}\boldsymbol{{z}}^{\mathrm{2}} \:-\:\mathrm{1}\:+\:\mathrm{2}\boldsymbol{{z}}\:\sqrt{\mathrm{1}-\boldsymbol{{z}}^{\mathrm{2}} } \\ $$ Commented by MJS_new last updated on 04/Sep/21 $$\mathrm{I}\:\mathrm{get}\:{z}=\mathrm{sin}\:\frac{\pi}{\mathrm{5}}\:=\frac{\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}} \\…