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Question-129825

Question Number 129825 by 0731619177 last updated on 19/Jan/21 Answered by Olaf last updated on 20/Jan/21 $$\mathrm{Let}\:{u}_{\mathrm{0}} \:=\:\mathrm{0}\:\mathrm{and}\:{u}_{{n}} \:=\:\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}…}}},\:{n}\:\geqslant\:\mathrm{1} \\ $$$${u}_{{n}+\mathrm{1}} \:=\:\sqrt{\mathrm{2}+{u}_{{n}} } \\ $$$$\mathrm{By}\:\mathrm{induction}\::…

x-iy-3-6-2-7-i-1-7-i-find-x-y-

Question Number 129809 by mohammad17 last updated on 19/Jan/21 $$\left({x}+{iy}\right)^{\mathrm{3}} =\frac{−\mathrm{6}+\mathrm{2}\sqrt{\mathrm{7}}{i}}{\mathrm{1}−\sqrt{\mathrm{7}}{i}}\:\:{find}\:{x},{y} \\ $$ Answered by Olaf last updated on 20/Jan/21 $$\left({x}+{iy}\:\right)^{\mathrm{3}} \:=\:\frac{−\mathrm{6}+\mathrm{2}\sqrt{\mathrm{7}}{i}}{\mathrm{1}−\sqrt{\mathrm{7}}{i}} \\ $$$$\mathrm{Let}\:{x}+{iy}\:=\:\rho{e}^{{i}\theta} \\…

2-5-1-3-2-5-1-3-9-x-5-12-x-4-2x-1-log-2-6x-2-11x-4-0-

Question Number 129785 by bramlexs22 last updated on 19/Jan/21 $$\:\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{2}−\sqrt{\mathrm{5}}}\:=? \\ $$$$\:\frac{\mathrm{9}^{\mathrm{x}} −\mathrm{5}.\mathrm{12}^{\mathrm{x}} +\:\mathrm{4}^{\mathrm{2x}+\mathrm{1}} }{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{6x}^{\mathrm{2}} −\mathrm{11x}+\mathrm{4}\right)}\:\leqslant\:\mathrm{0}\: \\ $$ Answered by EDWIN88 last updated on…

Question-64240

Question Number 64240 by harish kumar last updated on 16/Jul/19 Answered by Tanmay chaudhury last updated on 16/Jul/19 $$\mathrm{4}{x}^{\mathrm{2}} −{y}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{2}{y}−\mathrm{3}{xy} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{3}{xy}−{y}^{\mathrm{2}} +\mathrm{2}\left({x}−{y}\right)…