Question Number 27000 by abdo imad last updated on 01/Jan/18 $${P}\:{is}\:{a}\:{polynomial}\:{havng}\:{n}\:{roots}\:\left({x}_{{i}} \right)_{\mathrm{1}\leqslant{i}\leqslant{n}} \:\:{with}\:{x}_{{i}} \neq\:{x}_{{j}} \:{for}\:{i}\neq\:{j} \\ $$$${find}\:{the}\:{values}\:{of}\:\sum_{{k}\mathrm{1}} ^{{k}={n}} \frac{\mathrm{1}}{{x}−{x}_{{k}} }\:\:{and}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{\left({x}−{x}_{{k}} \right)^{\mathrm{2}} }\:. \\…
Question Number 27002 by math solver last updated on 01/Jan/18 Commented by moxhix last updated on 01/Jan/18 $${x}\neq\mathrm{0}\:\left(\because\mathrm{0}^{\mathrm{2}} +\mathrm{0}+\mathrm{1}\neq\mathrm{0}\right) \\ $$$$\frac{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{{x}}=\frac{\mathrm{0}}{{x}} \\ $$$${x}+\frac{\mathrm{1}}{{x}}=−\mathrm{1} \\…
Question Number 26999 by abdo imad last updated on 01/Jan/18 $${calculate}\:\prod_{{k}=\mathrm{1}} ^{{n}} {cos}\left(\frac{{a}}{\mathrm{2}^{{k}} }\right)\:\:{and}\mathrm{0}<{a}<\pi\:\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$${lim}_{{n}−>\propto} \:\sum_{{k}=\mathrm{1}} ^{{n}} {ln}\left({cos}\left(\frac{{a}}{\mathrm{2}^{{k}} }\right)\right). \\ $$ Answered by prakash…
Question Number 26997 by abdo imad last updated on 01/Jan/18 $${let}\:{give}\:\xi\:\in\mathbb{C}\:{and}\:\xi^{{n}} =\mathrm{1}\:\left(\xi\:{is}\:{the}\:{n}^{{me}} \:{root}\:{of}\:\mathrm{1}\right) \\ $$$${simplify}\:\:{A}=\:\mathrm{1}+\xi^{{p}} +\xi^{\mathrm{2}{p}} +…\:+\xi^{\left({n}−\mathrm{1}\right){p}} \\ $$$${and}\:{B}=\:\mathrm{1}+\mathrm{2}\xi\:+\mathrm{3}\xi^{\mathrm{2}} +…+{n}\xi^{{n}−\mathrm{1}} . \\ $$ Commented by…
Question Number 26998 by abdo imad last updated on 01/Jan/18 $${smlify}\:{X}=\:\:\prod_{{p}=\mathrm{2}} ^{{n}} \frac{{p}^{\mathrm{3}} −\mathrm{1}}{{p}^{\mathrm{3}} \:+\mathrm{1}}\:{by}\:{using}\:\mathrm{1},{j},{j}^{\mathrm{2}} {and}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} . \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 158067 by ajfour last updated on 30/Oct/21 $$\:\:{f}\left({x}\right)=\left(\frac{\mathrm{4}}{\mathrm{9}}\right)\frac{\left(\omega{x}+\mathrm{2}\right)^{\mathrm{2}} }{\left[\left(\omega{x}+\mathrm{11}\right)^{\mathrm{2}} −\mathrm{117}\right]} \\ $$$$\:\:\:\:\:+\left(\frac{\mathrm{8}}{\mathrm{5}}\right)\frac{\mathrm{1}}{\left[\left(\omega{x}+\mathrm{11}\right)^{\mathrm{2}} −\mathrm{117}\right]} \\ $$$${find}\:{real}\:{x}\:{such}\:{that}\:{f}\left({x}\right) \\ $$$${is}\:{real}.\:\:{I}\:{dont}\:{want}\:{x}=−\mathrm{2}. \\ $$ Terms of Service Privacy…
Question Number 158065 by zainaltanjung last updated on 30/Oct/21 Answered by Rasheed.Sindhi last updated on 30/Oct/21 $$\:\:\:\:\:\:\:\sqrt{\mathrm{2}+\mathrm{2}\sqrt{\frac{\mathrm{3}}{\mathrm{4}}}} \\ $$$$=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:={p}+{q}\sqrt{\mathrm{3}} \\ $$$$=\mathrm{2}+\sqrt{\mathrm{3}}\:={p}^{\mathrm{2}} +\mathrm{3}{q}^{\mathrm{2}} +\mathrm{2}{pq}\sqrt{\mathrm{3}} \\ $$$$\:\:\:\:{p}^{\mathrm{2}}…
Question Number 158035 by HongKing last updated on 30/Oct/21 Answered by mr W last updated on 30/Oct/21 $${say}\:{BC}=\mathrm{1} \\ $$$$\frac{{BD}}{\mathrm{sin}\:\mathrm{9}}=\frac{\mathrm{1}}{\mathrm{sin}\:\left(\mathrm{3}+\mathrm{9}\right)}\: \\ $$$$\Rightarrow{BD}=\frac{\mathrm{sin}\:\mathrm{9}}{\mathrm{sin}\:\mathrm{12}} \\ $$$$\frac{{BA}}{\mathrm{sin}\:\left(\mathrm{9}+\mathrm{45}\right)}=\frac{\mathrm{1}}{\mathrm{sin}\:\left(\mathrm{27}+\mathrm{3}+\mathrm{9}+\mathrm{45}\right)} \\…
Question Number 158039 by HongKing last updated on 30/Oct/21 $$\mathrm{f}\:\left(\frac{\mathrm{x}\:+\:\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{x}\:+\:\mathrm{2}\:\:\Rightarrow\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$ Answered by puissant last updated on 30/Oct/21 $${y}=\frac{{x}+\mathrm{1}}{\mathrm{2}}\:\rightarrow\:{x}=\mathrm{2}{y}−\mathrm{1} \\ $$$$\Rightarrow\:{f}\left({x}\right)\:=\:\left(\mathrm{2}{x}−\mathrm{1}\right)+\mathrm{2}\:=\:\mathrm{2}{x}+\mathrm{1} \\ $$ Answered…
Question Number 92488 by hmamarques1994@gmail.com last updated on 07/May/20 $$\:\left(\mathrm{3x}\right)^{\mathrm{log}_{\mathrm{b}} \:\mathrm{3}} \:=\:\left(\mathrm{5x}\right)^{\mathrm{log}_{\mathrm{b}} \:\mathrm{5}} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$ Commented by jagoll last updated on…