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Category: Algebra

8x-3-6x-1-0-Solves-

Question Number 11672 by @ANTARES_VY last updated on 29/Mar/17 $$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{Solves}}… \\ $$ Commented by mrW1 last updated on 29/Mar/17 $${see}\:{general}\:{solution}: \\ $$…

8x-3-6x-1-0-Solves-equation-x-1-x-2-

Question Number 11661 by @ANTARES_VY last updated on 29/Mar/17 $$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{Solves}}…\:\:\boldsymbol{\mathrm{equation}} \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{1}} =?\:\:\:\:\:\boldsymbol{\mathrm{x}}_{\mathrm{2}} =? \\ $$ Answered by Joel576 last updated on…

Let-k-be-non-negative-real-numbers-and-n-N-1-Prove-that-4-k-4-k-12-k-12-k-2n-n-1-k-2n-n-1-k-n-k-1-n-1-k-1-

Question Number 142710 by loveineq last updated on 04/Jun/21 $$\mathrm{Let}\:{k}\:\mathrm{be}\:\mathrm{non}-\mathrm{negative}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{and}\:{n}\:\in\:\mathrm{N}^{+} \geqslant\mathrm{1}.\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\frac{\mathrm{4}−{k}}{\mathrm{4}+{k}}\right)\left(\frac{\mathrm{12}−{k}}{\mathrm{12}+{k}}\right)…\left[\frac{\mathrm{2}{n}\left({n}+\mathrm{1}\right)−{k}}{\mathrm{2}{n}\left({n}+\mathrm{1}\right)+{k}}\right]\:\leqslant\:\frac{{n}+{k}+\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({k}+\mathrm{1}\right)} \\ $$$$ \\ $$ Answered by loveineq last updated on…

p-x-1-p-x-1-4x-2-2x-10-p-x-

Question Number 11628 by uni last updated on 29/Mar/17 $$\mathrm{p}\left(\mathrm{x}−\mathrm{1}\right)+\mathrm{p}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{4x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=? \\ $$ Answered by sandy_suhendra last updated on 29/Mar/17 $$\mathrm{let}\:\mathrm{p}\left(\mathrm{x}\right)=\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c} \\…

If-f-x-x-3-x-1-and-h-x-f-f-f-f-2022-times-f-x-then-h-1-

Question Number 142674 by Snail last updated on 03/Jun/21 $${If}\:{f}\left({x}\right)=\frac{{x}−\mathrm{3}}{{x}+\mathrm{1}}\:{and}\:{h}\left({x}\right)={f}\left({f}\left({f}\left({f}\left(..\mathrm{2022}\:{times}\left({f}\left({x}\right)\right)\right)\right)\right)\right) \\ $$$${then}\:\:\:{h}\left(\mathrm{1}\right)\:=? \\ $$ Answered by iloveisrael last updated on 04/Jun/21 $${f}\left({f}\left({x}\right)\right)=\frac{\frac{{x}−\mathrm{3}}{{x}+\mathrm{1}}−\mathrm{3}}{\frac{{x}−\mathrm{3}}{{x}+\mathrm{1}}+\mathrm{1}}\:=\:\frac{{x}−\mathrm{3}−\mathrm{3}{x}−\mathrm{3}}{{x}−\mathrm{3}+{x}+\mathrm{1}} \\ $$$${f}\left({f}\left({x}\right)\right)=\:\frac{−\mathrm{2}{x}−\mathrm{6}}{\mathrm{2}{x}−\mathrm{2}}\:=\:\frac{−{x}−\mathrm{3}}{{x}−\mathrm{1}}={f}^{−\mathrm{1}} \left({x}\right)…

lim-n-n-6-n-6-n-

Question Number 142668 by mathdanisur last updated on 03/Jun/21 $$\underset{{n}\rightarrow\infty} {{lim}}\left(\frac{{n}+\mathrm{6}}{{n}}\right)^{\frac{\mathrm{6}}{{n}}} =\:? \\ $$ Commented by iloveisrael last updated on 04/Jun/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{n}+\mathrm{6}}{{n}}\right)^{\frac{\mathrm{6}}{{n}}} \:= \\…