Question Number 41622 by math khazana by abdo last updated on 10/Aug/18 $${let}\:{z}_{\mathrm{1}} \:{and}\:{z}_{\mathrm{2}} \:{the}\:{roots}\:{of}\:{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}=\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{z}_{\mathrm{1}} ^{\mathrm{3}} \:+{z}_{\mathrm{2}} ^{\mathrm{3}} \:\:\:{then}\:\:\frac{\mathrm{1}}{{z}_{\mathrm{1}} ^{\mathrm{3}} }\:+\frac{\mathrm{1}}{{z}_{\mathrm{2}} ^{\mathrm{3}}…
Question Number 172688 by mr W last updated on 30/Jun/22 $$\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} \:\:{right}? \\ $$$$\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +\mathrm{4}^{\mathrm{3}} \:\:{right}? \\ $$…
Question Number 172687 by Rasheed.Sindhi last updated on 30/Jun/22 $$\mathrm{Sum}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms}: \\ $$$$\mathrm{7}+\mathrm{77}+\mathrm{777}+… \\ $$ Commented by mr W last updated on 30/Jun/22 $${S}=\mathrm{1}+\mathrm{11}+\mathrm{111}+…+\underset{{n}\:{times}} {\mathrm{111}\centerdot\centerdot\centerdot\mathrm{1}} \\…
Question Number 107117 by Algoritm last updated on 08/Aug/20 Answered by mr W last updated on 08/Aug/20 $$\frac{\mathrm{2}\:\mathrm{sin}\:\mathrm{2}°+\mathrm{4}\:\mathrm{sin}\:\mathrm{4}°+…+\mathrm{180}\:\mathrm{sin}\:\mathrm{180}°}{\mathrm{9}} \\ $$$${or} \\ $$$$\frac{\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{4}°+…+\mathrm{180}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{180}°}{\mathrm{9}}\:?…
Question Number 172631 by Mikenice last updated on 29/Jun/22 Commented by mr W last updated on 29/Jun/22 $${x}!=\left({x}+\mathrm{1}\right){x}\left({x}−\mathrm{1}\right) \\ $$$${x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)!=\left({x}+\mathrm{1}\right){x}\left({x}−\mathrm{1}\right) \\ $$$$\left({x}−\mathrm{2}\right)!={x}+\mathrm{1} \\ $$$${let}\:{u}={x}−\mathrm{2} \\…
Question Number 172609 by Mikenice last updated on 29/Jun/22 Answered by Rasheed.Sindhi last updated on 29/Jun/22 $$\mathrm{4}^{{x}} +\mathrm{4}^{{x}} =\mathrm{4}^{\mathrm{8}} ……………\left({i}\right) \\ $$$${x}+{y}=\mathrm{20}……………..\left({ii}\right) \\ $$$${y}+{y}=? \\…
Question Number 172611 by Mikenice last updated on 29/Jun/22 Answered by MJS_new last updated on 29/Jun/22 $$\mathrm{I}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{but}\:\mathrm{I}\:\mathrm{guess}\:\mathrm{ir}'\mathrm{s}\:\mathrm{meant}\:\mathrm{to}\:\mathrm{be} \\ $$$$\frac{{x}^{\mathrm{2}} +\mathrm{4}{x}}{\mathrm{3}}+\frac{\mathrm{84}}{{x}^{\mathrm{2}} +\mathrm{4}{x}}=\mathrm{11} \\ $$$${t}={x}^{\mathrm{2}} +\mathrm{4}{x} \\…
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Question Number 172599 by Mikenice last updated on 29/Jun/22 Answered by Rasheed.Sindhi last updated on 29/Jun/22 $$\underset{\left({i}\right)} {\underbrace{\mathrm{8}{y}^{{x}} −{y}^{\mathrm{2}{x}} =\mathrm{16}}}\:,\:\underset{\left({ii}\right)} {\underbrace{\mathrm{2}^{{x}} ={y}^{\mathrm{2}} }}\:;\:\:\:\:\:{x}=?,{y}=? \\ $$$$\left({i}\right)\Rightarrow\mathrm{8}\left({y}^{\mathrm{2}}…
Question Number 41522 by Tawa1 last updated on 09/Aug/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\:\:\mathrm{26}\:−\:\mathrm{15}\sqrt{\mathrm{3}} \\ $$ Commented by math khazana by abdo last updated on 10/Aug/18 $${inside}\:{C}\:\:{z}^{\mathrm{3}} =\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}\:\:{let}\:{z}={x}+{iy}\:\Rightarrow \\…