Menu Close

Category: Algebra

solve-x-2-3x-6y-xy-5x-4y-

Question Number 88160 by john santu last updated on 08/Apr/20 $${solve}\::\:{x}^{\mathrm{2}} \:=\:\mathrm{3}{x}\:+\:\mathrm{6}{y}\:;\:{xy}\:=\:\mathrm{5}{x}\:+\:\mathrm{4}{y} \\ $$ Commented by john santu last updated on 08/Apr/20 $${y}\:=\:\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}}{\mathrm{6}}\:\:;\:{y}\left({x}−\mathrm{4}\right)\:=\:\mathrm{5}{x} \\…

If-1-x-n-C-0-C-1-x-C-2-x-2-C-3-x-3-C-n-x-n-prove-that-2-2-1-2-C-0-2-3-2-3-C-1-2-4-3-4-C-2-2-n-2-n-1-n-2-C-n-3-n-2-2n-5-

Question Number 22618 by Tinkutara last updated on 21/Oct/17 $${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:…\:+\:{C}_{{n}} {x}^{{n}} ,\:{prove}\:{that} \\ $$$$\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{1}.\mathrm{2}}{C}_{\mathrm{0}} \:+\:\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{2}.\mathrm{3}}{C}_{\mathrm{1}}…

i-1-i-xi-i-x-x-

Question Number 153682 by EDWIN88 last updated on 09/Sep/21 $$\:\left(\sqrt[{{i}}]{{i}}\:\right)^{{xi}} \:=\:{i}^{{x}} \: \\ $$$$\:\:{x}=?\: \\ $$ Answered by MJS_new last updated on 09/Sep/21 $$\mathrm{lhs}\:\mathrm{i}=\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{2}}} \:\Rightarrow\:\sqrt[{\mathrm{i}}]{\mathrm{i}}=\mathrm{e}^{\frac{\pi}{\mathrm{2}}}…

Question-88141

Question Number 88141 by A8;15: last updated on 08/Apr/20 Answered by MJS last updated on 08/Apr/20 $$\mathrm{squaring}\:\mathrm{and}\:\mathrm{transforming}\:\mathrm{3}\:\mathrm{times}\:\mathrm{leads}\:\mathrm{to} \\ $$$${x}^{\mathrm{8}} −\mathrm{28}{x}^{\mathrm{6}} +\mathrm{238}{x}^{\mathrm{4}} −\mathrm{588}{x}^{\mathrm{2}} +\mathrm{128}{x}−\mathrm{7}=\mathrm{0} \\ $$$$\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{factorized}…

Question-153638

Question Number 153638 by mathdanisur last updated on 08/Sep/21 Commented by EDWIN88 last updated on 09/Sep/21 $${b}×{c}=\mathrm{12}{a} \\ $$$$\Rightarrow{a}^{\mathrm{2}} ={b}^{\mathrm{2}} +{c}^{\mathrm{2}} \\ $$$$\Rightarrow{a}^{\mathrm{2}} =\left({b}+{c}\right)^{\mathrm{2}} −\mathrm{24}{a}…

Question-153629

Question Number 153629 by mathdanisur last updated on 08/Sep/21 Commented by benhamimed last updated on 09/Sep/21 $$\mathrm{1}+{x}+…+{x}^{{n}} =\frac{\mathrm{1}−{x}^{{n}} }{\mathrm{1}−{x}}=\frac{\frac{{t}^{{n}} −\mathrm{1}}{{t}^{{n}} }}{\frac{{t}−\mathrm{1}}{{t}}}=\frac{\left({t}^{{n}} −\mathrm{1}\right)}{{t}^{{n}−\mathrm{1}} \left({t}−\mathrm{1}\right)}\:\:\:\:{tq}\:{x}=\frac{\mathrm{1}}{{t}} \\ $$$${si}\:{x}=\frac{\mathrm{1}}{\mathrm{2021}}\:\:;{t}=\mathrm{2021}…