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AlgebraQuestion and Answers: Page 93
Question Number 174062 Answers: 2 Comments: 2
$$\mathrm{find}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\:\mathrm{such}\:\mathrm{that}\:\:\:\:\mathrm{p}^{\mathrm{2}} \:\:−\:\:\mathrm{p}\:\:\:\:=\:\:\:\mathrm{37q}^{\mathrm{2}} \:\:−\:\:\mathrm{q} \\ $$
Question Number 174059 Answers: 2 Comments: 3
$${if}\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +\mathrm{3}{xy}=\mathrm{1},\:{then}\:{x}+{y}=? \\ $$
Question Number 174057 Answers: 0 Comments: 1
Question Number 174036 Answers: 1 Comments: 0
$$\:\:\mathrm{Factorize}\:{x}^{\mathrm{2}} \:+\:\sqrt{\mathrm{2}{x}\:}+\:{x}\:+\:\mathrm{2} \\ $$
Question Number 174029 Answers: 1 Comments: 1
$${x}+{y}=\mathrm{1} \\ $$$${x}^{\mathrm{5}} +{xy}+{y}^{\mathrm{5}} ={x}^{\mathrm{2}} {y}^{\mathrm{2}\:\:\:\:\:\:} \\ $$$${faind}\:{the}\:{volue}\:{of}\:\:\:{x}^{\mathrm{2022}} +{xy}+{y}^{\mathrm{2022}} =? \\ $$
Question Number 174023 Answers: 2 Comments: 1
Question Number 173997 Answers: 2 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{If}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt[{\mathrm{3}}]{{x}}\:−\:\mathrm{3}\:=\:\sqrt[{\mathrm{3}}]{{x}−\mathrm{36}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{then}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{x}^{\:\mathrm{2}} −\mathrm{1}}{{x}}\:=\:?\: \\ $$$$\:\:\:\:\:\:\: \\ $$
Question Number 173992 Answers: 1 Comments: 1
Question Number 173984 Answers: 0 Comments: 0
Question Number 173981 Answers: 2 Comments: 0
Question Number 173978 Answers: 1 Comments: 0
$$\mathrm{Solve}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\mathrm{x}+\frac{\mathrm{3x}−\mathrm{y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }=\mathrm{3} \\ $$$$\mathrm{y}−\frac{\mathrm{x}+\mathrm{3y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }=\mathrm{0} \\ $$$$ \\ $$
Question Number 173970 Answers: 1 Comments: 3
Question Number 173948 Answers: 1 Comments: 4
Question Number 173946 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:{If}\:\mathrm{3}{sin}\left({x}\right)+\mathrm{4}{cos}\left({y}\right)−\mathrm{3}{sin}\left({y}\right)=\mathrm{8} \\ $$$$\:\:\:{then}\:..\:\:\:\:{sin}\left({x}\right)\:+\:{sin}\left({y}\right)=? \\ $$$$ \\ $$$$ \\ $$
Question Number 173933 Answers: 1 Comments: 1
Question Number 173958 Answers: 0 Comments: 0
Question Number 173926 Answers: 2 Comments: 3
$$ \\ $$$$\:\:\:\:\:{Q}: \\ $$$$\:\:\:\:\:\:\:{a}_{\:{n}\:} \:\:{is}\:{an}\:{arithmatic}\:{sequence}. \\ $$$$\:\:\:\:\:\:\:\:\:\:{a}\:\left(\:{first}\:{term}\right)\:{and}\:\:{d}\:\left({difference}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:{such}\:{that}\:,\:\:{a}_{\:{a}} \:+\:{a}_{\:{d}} \:=\:{a}_{\:{ad}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{find}\:\:\::\:\:\:\:{a}_{\:{n}} \:\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:{note}:\:\:{a}\:\:,\:\:{d}\:\:\:\in\:\mathbb{N}\:\: \\ $$$$\:\:\:\:\:\:\: \\ $$
Question Number 173923 Answers: 1 Comments: 1
Question Number 173917 Answers: 0 Comments: 2
$${prove}: \\ $$$$\left(−\mathrm{1}\right)! \\ $$
Question Number 173956 Answers: 0 Comments: 1
Question Number 173889 Answers: 0 Comments: 1
$${the}\:{anser}\:{is}\:{the}\:{folowing} \\ $$
Question Number 173887 Answers: 0 Comments: 0
Question Number 173882 Answers: 0 Comments: 0
Question Number 173871 Answers: 0 Comments: 1
$$\mathrm{2}^{{x}} \centerdot\mathrm{3}^{{y}} =\mathrm{4} \\ $$$$\mathrm{2}^{{y}} \centerdot\mathrm{3}^{{x}} =\mathrm{6}\:\:\:\:\:\:\:{prove}\:{that}\:\:{xy}={z}\left({z}+\mathrm{1}\right) \\ $$$$\mathrm{6}^{{z}} =\mathrm{2} \\ $$
Question Number 173869 Answers: 2 Comments: 2
$$ \\ $$$$\:{If},\:\:\:\left(\:\frac{\sqrt{\mathrm{10}}\:+\sqrt{\mathrm{6}}+\mathrm{2}}{\:\sqrt{\mathrm{5}}\:−\sqrt{\mathrm{3}\:}\:+\:\sqrt{\mathrm{2}}}\:\right)^{\:\mathrm{2}} =\:{a}\:+\:\sqrt{{b}} \\ $$$$\:\:\:\:\:\:\:\:{then}.\:\:\:\:\:\:\:\:{a}\:\:,\:\:\:{b}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$
Question Number 173864 Answers: 0 Comments: 0
$$\:\:\:\:\sqrt{{x}}\:\geqslant\:\frac{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{2}{x}−\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}} \\ $$
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