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Category: Algebra

Question-63678

Question Number 63678 by aliesam last updated on 07/Jul/19 Commented by Prithwish sen last updated on 07/Jul/19 $$\mathrm{Putting}\:\mathrm{x}=\mathrm{0}\:\mathrm{we}\:\mathrm{get}\:\mathrm{a}\:\mathrm{solution}. \\ $$$$\mathrm{Now}\:\mathrm{as}\:\mathrm{the}\:\mathrm{left}\:\mathrm{hand}\:\mathrm{side}\:\mathrm{is}\:\mathrm{an}\:\mathrm{increasing}\: \\ $$$$\mathrm{function}\:\mathrm{and}\:\mathrm{the}\:\mathrm{right}\:\mathrm{hand}\:\mathrm{side}\:\mathrm{is}\:\mathrm{a}\:\mathrm{decreasing}\: \\ $$$$\mathrm{function}\:\mathrm{then}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{only}\:\mathrm{1}\:\mathrm{solution} \\…

Question-63642

Question Number 63642 by bshahid010@gmail.com last updated on 06/Jul/19 Commented by kaivan.ahmadi last updated on 06/Jul/19 $$\left({x}+\mathrm{2}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}\right)=\mathrm{0}\Rightarrow \\ $$$${x}=−\mathrm{2}\Rightarrow\gamma=−\mathrm{2}\Rightarrow\gamma^{\mathrm{2}} =\mathrm{4} \\ $$$$\alpha,\beta\:{are}\:{the}\:{roots}\:{of}\:{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}=\mathrm{0} \\…

4-x-44-1-5-1-2-x-1-7-1-3-8-336-x-

Question Number 129148 by benjo_mathlover last updated on 13/Jan/21 $$\:\left[\:\sqrt[{\mathrm{5}}]{\mathrm{4}^{\mathrm{x}} +\mathrm{44}}\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}^{\mathrm{x}−\mathrm{1}} +\mathrm{7}}}\:\right]^{\mathrm{8}} =\:\mathrm{336} \\ $$$$\:\mathrm{x}\:=? \\ $$ Commented by liberty last updated on 13/Jan/21 $$\mathrm{nice}:!\:\mathrm{question}…

32x-3-48x-2-22x-3-0-

Question Number 63602 by pavithra last updated on 06/Jul/19 $$\mathrm{32}{x}^{\mathrm{3}} −\mathrm{48}{x}^{\mathrm{2}} −\mathrm{22}{x}−\mathrm{3}=\mathrm{0} \\ $$ Answered by MJS last updated on 06/Jul/19 $${x}^{\mathrm{3}} −\frac{\mathrm{3}}{\mathrm{2}}{x}^{\mathrm{2}} −\frac{\mathrm{11}}{\mathrm{16}}{x}−\frac{\mathrm{3}}{\mathrm{32}}=\mathrm{0} \\…

prove-that-k-1-1-k-2k-1-2-2ln-2-

Question Number 63574 by Tawa1 last updated on 05/Jul/19 $$\mathrm{prove}\:\mathrm{that}\:\:\:\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{2k}\:+\:\mathrm{1}\right)}\:\:=\:\:\mathrm{2}\:−\:\mathrm{2ln}\left(\mathrm{2}\right) \\ $$ Commented by mathmax by abdo last updated on 05/Jul/19 $${the}\:{H}_{{n}} \:{method}\:\:{let}\:{S}_{{n}}…