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Category: Algebra

Given-a-b-c-real-and-positive-numbers-and-a-b-c-1-Find-the-minimum-value-of-a-b-abc-

Question Number 22154 by Joel577 last updated on 12/Oct/17 $$\mathrm{Given}\:{a},{b},{c}\:\mathrm{real}\:\mathrm{and}\:\mathrm{positive}\:\mathrm{numbers},\:\mathrm{and} \\ $$$${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{1} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\frac{{a}\:+\:{b}}{{abc}} \\ $$ Answered by ajfour last updated on 12/Oct/17 $${let}\:{a}={cx}\:\:\:\:{and}\:\:{b}={cy} \\…

If-f-R-R-is-a-polynomial-function-which-satisfy-the-equation-f-f-x-f-x-12x-x-R-then-find-f-x-

Question Number 22133 by Tinkutara last updated on 11/Oct/17 $$\mathrm{If}\:{f}\::\:{R}^{+} \:\rightarrow\:{R}^{+} \:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{function} \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\:{f}\left({f}\left({x}\right)\right)\:+ \\ $$$${f}\left({x}\right)\:=\:\mathrm{12}{x}\:\forall\:{x}\:\in\:{R}^{+} ,\:\mathrm{then}\:\mathrm{find}\:{f}\left({x}\right). \\ $$ Commented by Rasheed.Sindhi last updated on…

Question-153203

Question Number 153203 by mathdanisur last updated on 05/Sep/21 Answered by Kamel last updated on 05/Sep/21 $${f}\left({x}\right)=\frac{\mathrm{1}−\sqrt{\mathrm{1}−\mathrm{2}{x}}}{\mathrm{2}},{f}_{{n}} ^{−\mathrm{1}} =\underset{…………… {n}\:{times} ………} {{f}^{−\mathrm{1}} \circ{f}^{−\mathrm{1}} \circ{f}^{−\mathrm{1}} \circ…\circ{f}^{−\mathrm{1}}…

1-sin-1-8-pi-i-cos-1-8-pi-1-sin-1-8-pi-i-cos-1-8-pi-

Question Number 87656 by M±th+et£s last updated on 05/Apr/20 $$\frac{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi+{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi−{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}=? \\ $$ Commented by Tony Lin last updated on 05/Apr/20 $${let}\:{sin}\frac{\pi}{\mathrm{8}}+{icos}\frac{\pi}{\mathrm{8}}={z}\:,\mid{z}\mid=\mathrm{1} \\ $$$$\frac{\mathrm{1}+{z}}{\mathrm{1}+\bar {{z}}} \\…

cosh-15-

Question Number 22102 by Parvez akhter last updated on 11/Oct/17 $$\mathrm{cosh}\:\left(\mathrm{15}\right) \\ $$ Answered by $@ty@m last updated on 11/Oct/17 $$\mathrm{cos}\:{hx}=\frac{{e}^{{x}} +{e}^{−{x}} }{\mathrm{2}} \\ $$$$\mathrm{cos}\:{h}\left(\mathrm{15}\right)=\frac{{e}^{\mathrm{15}}…

Question-153168

Question Number 153168 by liberty last updated on 05/Sep/21 Answered by EDWIN88 last updated on 05/Sep/21 $${let}\:{y}={u}^{\mathrm{2}} \:\&\:{x}={v}^{\mathrm{2}} \\ $$$$\left(\mathrm{1}\right)\sqrt{{v}^{\mathrm{2}} +{u}}\:+\sqrt{{v}^{\mathrm{2}} −{u}}\:=\:\mathrm{2} \\ $$$$\Rightarrow\mathrm{2}{v}^{\mathrm{2}} \:+\mathrm{2}\sqrt{{v}^{\mathrm{4}}…