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Category: Algebra

x-2-x-3-4x-1-10-for-x-R-

Question Number 128166 by bramlexs22 last updated on 05/Jan/21 $$\:\sqrt{\mathrm{x}−\mathrm{2}}\:+\:\sqrt{\mathrm{x}+\mathrm{3}}\:+\sqrt{\mathrm{4x}+\mathrm{1}}\:=\:\mathrm{10} \\ $$$$\:\mathrm{for}\:\mathrm{x}\in\mathbb{R}\: \\ $$ Answered by liberty last updated on 05/Jan/21 $$\:\sqrt{\mathrm{4x}+\mathrm{1}}\:=\:\left[\:−\sqrt{\mathrm{x}+\mathrm{3}}−\sqrt{\mathrm{x}−\mathrm{2}}+\mathrm{10}\:\right] \\ $$$$\:\mathrm{4x}+\mathrm{1}\:=\:\mathrm{2}\sqrt{\mathrm{x}−\mathrm{2}\:}\:\sqrt{\mathrm{x}+\mathrm{3}}\:−\mathrm{20}\sqrt{\mathrm{x}+\mathrm{3}}\:+\mathrm{2x}\:−\mathrm{20}\sqrt{\mathrm{x}−\mathrm{2}}\:+\mathrm{101} \\…

4-lt-x-lt-5-a-x-3-2-x-4-b-x-4-1-x-a-b-

Question Number 128146 by sahnaz last updated on 04/Jan/21 $$\mathrm{4}<\mathrm{x}<\mathrm{5}\:\mathrm{a}=\sqrt{\mathrm{x}−\mathrm{3}+\mathrm{2}\sqrt{\mathrm{x}−\mathrm{4}}\:\:}\:\:\:\mathrm{b}=\sqrt{\mathrm{x}−\mathrm{4}}−\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{x}−\mathrm{a}×\mathrm{b}=? \\ $$ Answered by Fikret last updated on 04/Jan/21 $${a}=\sqrt{{x}−\mathrm{4}}+\mathrm{1} \\ $$$${b}=\sqrt{{x}−\mathrm{4}}−\mathrm{1} \\ $$$${a}.{b}={x}−\mathrm{5} \\…

If-f-x-1-x-x-4-1-x-4-find-f-5-

Question Number 128132 by I want to learn more last updated on 04/Jan/21 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}}\right)\:\:\:=\:\:\:\mathrm{x}^{\mathrm{4}} \:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }\:,\:\:\:\:\:\mathrm{find}\:\:\mathrm{f}\left(\mathrm{5}\right) \\ $$ Answered by Olaf last updated on 04/Jan/21…

someone-help-cheking-this-x-3-x-c-let-x-p-2q-q-2p-p-q-p-3-8q-3-6pq-p-2q-q-3-8p-3-6pq-q-2p-3-p-2q-q-2p-p-2q-q-2p-p-2q-q-2p-c-7-p-3-q-3-6pq

Question Number 128090 by ajfour last updated on 04/Jan/21 $${someone}\:{help}\:{cheking}\:{this}: \\ $$$$\:\:\:\:{x}^{\mathrm{3}} ={x}+{c}\:\: \\ $$$${let}\:\:{x}=\left({p}−\mathrm{2}{q}\right)+\left({q}−\mathrm{2}{p}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:=\:−\left({p}+{q}\right) \\ $$$${p}^{\mathrm{3}} −\mathrm{8}{q}^{\mathrm{3}} −\mathrm{6}{pq}\left({p}−\mathrm{2}{q}\right)+ \\ $$$${q}^{\mathrm{3}} −\mathrm{8}{p}^{\mathrm{3}} −\mathrm{6}{pq}\left({q}−\mathrm{2}{p}\right)+…

Question-128065

Question Number 128065 by 0731619177 last updated on 04/Jan/21 Commented by mnjuly1970 last updated on 04/Jan/21 $${lim}_{{n}\rightarrow\infty\:\:\:} \underset{{k}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$$${lim}_{{n}\rightarrow\infty} \left(\underset{{k}=\mathrm{1}}…

n-0-1-n-8n-3-

Question Number 128048 by bramlexs22 last updated on 04/Jan/21 $$\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{8n}+\mathrm{3}}\:=? \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\mathrm{L}\left(\lambda,\alpha,{s}\right)\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{e}^{\mathrm{2}{i}\pi\lambda{n}}…