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AlgebraQuestion and Answers: Page 267
Question Number 84293 Answers: 1 Comments: 0
$${solve}\:{in}\:{R} \\ $$$${x}^{\left[{x}\right]} +{x}^{\mathrm{2}−\left[{x}\right]} ={x}^{\mathrm{2}} +\mathrm{1} \\ $$
Question Number 84188 Answers: 0 Comments: 4
$$\mathrm{if}\:\mathrm{2x}+\mathrm{3y}\:=\:\mathrm{2020}? \\ $$$$\mathrm{find}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{3x}+\mathrm{2y}\:\mathrm{for}\:\mathrm{x}\:\mathrm{and}\:\mathrm{natural} \\ $$$$\mathrm{number} \\ $$
Question Number 84182 Answers: 2 Comments: 0
$${Find}\:{the}\:{number}\:{of}\:{solutions}\:{for} \\ $$$${positive}\:{integers}\:\left({x},{y},{z}\right)\:{satisfying} \\ $$$$\boldsymbol{{x}}+\mathrm{2}\boldsymbol{{y}}+\mathrm{3}\boldsymbol{{z}}=\boldsymbol{{n}}. \\ $$
Question Number 84126 Answers: 1 Comments: 0
$$\int\frac{\mathrm{5}−{x}}{\mathrm{1}+\sqrt{\left({x}−\mathrm{4}\right)}}\boldsymbol{{dx}} \\ $$
Question Number 84109 Answers: 1 Comments: 2
Question Number 84047 Answers: 2 Comments: 0
$$\mathrm{how}\:\mathrm{many}\: \\ $$$$\mathrm{natural}\:\mathrm{solution}\:\mathrm{are}\:\mathrm{there}\:\mathrm{for}\: \\ $$$${x}^{\mathrm{2}} \:−\:{y}\:!\:=\:\mathrm{2019}\:. \\ $$
Question Number 84014 Answers: 0 Comments: 1
$${find}\:{the}\:{no}.\:{of}\:{positivve} \\ $$$${integral}\:{solutions}\:{of} \\ $$$${x}+{y}+\mathrm{2}{z}=\mathrm{89} \\ $$$${x}>\mathrm{10} \\ $$$${y}>\mathrm{20} \\ $$$${z}>\mathrm{2} \\ $$
Question Number 84002 Answers: 0 Comments: 0
$$\frac{{sin}\left({x}\right)}{\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+{cos}^{\mathrm{2}} \left({x}\right)}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}={csc}\left({x}\right)\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+{cos}^{\mathrm{2}} \left({x}\right)} \\ $$$${show}\:{that} \\ $$$${x}=\left\{\frac{\pi}{\mathrm{2}}+\mathrm{2}\pi{n}\right\}\:{and}\:{x}=\left\{{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{3}}\right)−\pi+\mathrm{2}\pi{n}\right\} \\ $$$${and}\:{x}=\left\{−{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{3}}\right)+\mathrm{2}\pi{n}\right\} \\ $$$$ \\ $$
Question Number 84005 Answers: 2 Comments: 4
$${find}\:{atleast}\:\mathrm{7}\:{solutions} \\ $$$${of}\:{the}\:{equation}. \\ $$$$\mathrm{900}{x}+\mathrm{7689}{y}=\mathrm{109876} \\ $$$${CAN}\:{ANYONE}\:{SOLVE} \\ $$$${THIS} \\ $$$${now}\:{lets}\:{find}\:\mathrm{7}\:{integral} \\ $$$${solutions} \\ $$
Question Number 83941 Answers: 1 Comments: 0
$$\mathrm{If}\:\sqrt[{\mathrm{3}}]{\mathrm{2}\:}\:+\:\sqrt[{\mathrm{3}\:}]{\mathrm{4}}\:+\:\sqrt[{\mathrm{3}\:}]{\mathrm{8}\:}\:=\:\mathrm{x}\: \\ $$$$\mathrm{then}\:\mathrm{x}^{\mathrm{3}} −\mathrm{6x}^{\mathrm{2}} +\mathrm{6x}+\mathrm{6}\:=\:? \\ $$
Question Number 83931 Answers: 1 Comments: 1
$$\frac{\mathrm{1}}{\left(\sqrt{\mathrm{1}}+\sqrt{\mathrm{2}}\right)\left(\sqrt[{\mathrm{4}\:}]{\mathrm{1}}+\sqrt[{\mathrm{4}\:}]{\mathrm{2}}\right)}\:+\:\frac{\mathrm{1}}{\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}\right)\left(\sqrt[{\:\mathrm{4}}]{\mathrm{2}}+\sqrt[{\mathrm{4}\:}]{\mathrm{3}}\right)}\:+ \\ $$$$\frac{\mathrm{1}}{\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}\right)\left(\sqrt[{\mathrm{4}\:}]{\mathrm{3}}+\sqrt[{\mathrm{4}\:}]{\mathrm{4}}\right)}\:+\:...\:+\:\frac{\mathrm{1}}{\left(\sqrt{\mathrm{255}}+\sqrt{\mathrm{256}}\right)\left(\sqrt[{\mathrm{4}\:}]{\mathrm{255}}+\sqrt[{\mathrm{4}\:}]{\mathrm{256}}\right)} \\ $$$$=\:...\: \\ $$
Question Number 83910 Answers: 2 Comments: 1
$$\mathrm{find}\:\mathrm{all}\:\mathrm{6}\:\mathrm{digit}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{are}\:\mathrm{not} \\ $$$$\mathrm{only}\:\mathrm{palindrome}\:\mathrm{but}\:\mathrm{also}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{495}. \\ $$
Question Number 83874 Answers: 1 Comments: 1
Question Number 83871 Answers: 0 Comments: 4
$$\mathrm{If}\:\mathrm{equation}\: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }+\sqrt{\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }+\sqrt{\mathrm{x}^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{3}\right)^{\mathrm{2}} }+\sqrt{\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{3}\right)^{\mathrm{2}} }=\mathrm{10}}\\{\mathrm{x}+\mathrm{2y}=\:\mathrm{5z}}\end{cases} \\ $$$$\mathrm{has}\:\mathrm{solution}\:\mathrm{is}\:\left(\mathrm{a},\mathrm{b},\mathrm{c}\right).\: \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{2b}+\mathrm{3c}\: \\ $$
Question Number 83834 Answers: 1 Comments: 2
Question Number 83824 Answers: 2 Comments: 1
Question Number 83822 Answers: 1 Comments: 1
Question Number 83791 Answers: 2 Comments: 2
$$\mathrm{Let}\:\mathrm{x},\:\mathrm{y}\:\mathrm{are}\:\mathrm{two}\:\mathrm{different}\:\mathrm{real} \\ $$$$\mathrm{numbers}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\sqrt{\mathrm{y}+\mathrm{4}}\:=\:\mathrm{x}−\mathrm{4}\:\mathrm{and}\:\sqrt{\mathrm{x}+\mathrm{4}}\:=\:\mathrm{y}−\mathrm{4}. \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} \:\mathrm{mod}\left(\mathrm{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{3}} \right)\:\mathrm{is} \\ $$
Question Number 83787 Answers: 1 Comments: 0
$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{abc}\:\mathrm{if}\: \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}^{\mathrm{2}} +\sqrt{\mathrm{2}^{\mathrm{3}} +\mathrm{2}^{\mathrm{4}} +\sqrt{...}}}}\:=\:\frac{\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}}{\mathrm{c}} \\ $$
Question Number 83767 Answers: 2 Comments: 1
Question Number 83759 Answers: 2 Comments: 3
$$\mathrm{3}^{{x}} \:\mathrm{8}^{\frac{{x}}{{x}+\mathrm{2}}} =\mathrm{6} \\ $$
Question Number 83721 Answers: 3 Comments: 8
Question Number 83674 Answers: 1 Comments: 1
Question Number 83672 Answers: 2 Comments: 0
$${x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:=\:\mathrm{51}\: \\ $$$${find}\:{x}\: \\ $$
Question Number 83608 Answers: 1 Comments: 4
$$\sqrt[{\mathrm{4}\:\:}]{\mathrm{17}+\mathrm{x}}\:+\:\sqrt[{\mathrm{4}\:\:}]{\mathrm{17}−\mathrm{x}}\:=\:\mathrm{2}\: \\ $$$$\mathrm{find}\:\mathrm{x}\: \\ $$
Question Number 83599 Answers: 0 Comments: 0
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