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Category: Algebra

If-x-2-y-2-9-4a-2-9b-2-16-then-maximum-value-of-4a-2-x-2-9b-2-y-2-12abxy-is-

Question Number 32629 by rahul 19 last updated on 29/Mar/18 $$\boldsymbol{{I}}{f}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{9}\:,\:\mathrm{4}{a}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} =\mathrm{16}, \\ $$$${then}\:\boldsymbol{{maximum}}\:{value}\:{of}\: \\ $$$$\mathrm{4}{a}^{\mathrm{2}} {x}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} {y}^{\mathrm{2}} −\mathrm{12}{abxy}\:{is}\:? \\ $$…

if-a-2b-2-b-2c-2-0-find-volve-b-c-a-3-abc-

Question Number 163651 by mathlove last updated on 09/Jan/22 $${if}\:\:\left({a}−\mathrm{2}{b}\right)^{\mathrm{2}} +\left({b}−\mathrm{2}{c}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:\:{volve}\:\:\frac{\left({b}+{c}−{a}\right)^{\mathrm{3}} }{{abc}}=? \\ $$ Commented by cortano1 last updated on 09/Jan/22 $$\left.\begin{matrix}{{a}=\mathrm{2}{b}\Rightarrow{b}=\frac{\mathrm{1}}{\mathrm{2}}{a}}\\{{b}=\mathrm{2}{c}\Rightarrow{c}=\frac{\mathrm{1}}{\mathrm{4}}{a}}\end{matrix}\right\}\:\Rightarrow\frac{−\frac{\mathrm{1}}{\mathrm{64}}{a}^{\mathrm{3}}…

The-set-of-values-of-a-for-which-all-the-solutions-of-the-equation-4sin-4-x-asin-2-x-3-0-are-real-and-distinct-is-

Question Number 32563 by rahul 19 last updated on 27/Mar/18 $$\boldsymbol{{T}}{he}\:{set}\:{of}\:{values}\:{of}\:'{a}'\:{for}\:{which}\: \\ $$$${all}\:{the}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{4sin}\:^{\mathrm{4}} {x}+{a}\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{3}=\mathrm{0}\:{are}\:{real}\:{and}\: \\ $$$${distinct}\:{is}\:? \\ $$ Commented by rahul 19…

x-2-y-2-3-x-3-3x-2-y-3xy-2-y-3-1-x-3-y-3-x-y-2-find-x-and-y-

Question Number 163632 by HongKing last updated on 08/Jan/22 $$\frac{\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{y}^{\mathrm{2}} \right)\centerdot\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \mathrm{y}\:+\:\mathrm{3xy}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{3}} }}\:=\:-\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\left(\mathrm{x}\:+\:\mathrm{y}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}} \\ $$ Answered…

x-1-x-3-x-3579-1-x-3579-

Question Number 163631 by HongKing last updated on 08/Jan/22 $$\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\sqrt{\mathrm{3}}\:\:\Rightarrow\:\mathrm{x}^{\mathrm{3579}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3579}} }\:=\:? \\ $$ Answered by MathsFan last updated on 09/Jan/22 $$\mathrm{x}^{\mathrm{2}} −\mathrm{x}\sqrt{\mathrm{3}}+\mathrm{1}=\mathrm{0}\:\rightarrow\:\mathrm{x}=\frac{{i}\pm\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\left(\frac{{i}\pm\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{3579}}…

The-coefficient-of-x-4-in-the-expansion-of-1-5x-9x-2-1-x-2-11-is-a-171-b-172-c-173-d-176-

Question Number 32543 by rahul 19 last updated on 27/Mar/18 $$\boldsymbol{{T}}{he}\:{coefficient}\:{of}\:{x}^{\mathrm{4}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left(\mathrm{1}+\mathrm{5}{x}+\mathrm{9}{x}^{\mathrm{2}} +…..\infty\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{11}} {is} \\ $$$$\left.{a}\right)\:\mathrm{171} \\ $$$$\left.{b}\right)\:\mathrm{172} \\ $$$$\left.{c}\right)\:\mathrm{173} \\ $$$$\left.{d}\right)\:\mathrm{176}…