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Category: Algebra

Question-7360

Question Number 7360 by rohit meena last updated on 24/Aug/16 Answered by Rasheed Soomro last updated on 25/Aug/16 $$\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{4}−{k}\right){x}^{\mathrm{2}} +\mathrm{2}\left({k}+\mathrm{2}\right){x}+\mathrm{8}{k}+\mathrm{1} \\ $$$${The}\:{value}\:{of}\:\:{k},{for}\:{which}\:{the}\:{above} \\…

Solve-the-simultaneous-equation-2x-y-z-8-i-x-2-y-2-2z-2-14-ii-3x-3-4y-3-z-3-195-iii-

Question Number 7330 by Tawakalitu. last updated on 23/Aug/16 $${Solve}\:{the}\:{simultaneous}\:{equation}\: \\ $$$$ \\ $$$$\mathrm{2}{x}\:\:+\:{y}\:\:−\:{z}\:=\:\mathrm{8}\:………\:\left({i}\right) \\ $$$${x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{z}^{\mathrm{2}} \:=\:\mathrm{14}\:\:……….\left({ii}\right) \\ $$$$\mathrm{3}{x}^{\mathrm{3}} \:+\:\mathrm{4}{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:=\:\mathrm{195}\:\:…………\:\left({iii}\right) \\…

Question-7331

Question Number 7331 by rohit meena last updated on 23/Aug/16 Commented by sandy_suhendra last updated on 24/Aug/16 $${for}\:{the}\:{simetric}\:{root},\:{like}\:{y}_{\mathrm{1}} =\mathrm{2}\alpha\:{and}\:{y}_{\mathrm{2}} =\mathrm{2}\beta,\:{we}\:{can}\:{use}\:{the}\:{subtitute}\:{method} \\ $$$${y}=\mathrm{2}{x}\:\Rightarrow{x}=\frac{\mathrm{1}}{\mathrm{2}}{y}\:{substitute}\:{to}\:{ax}^{\mathrm{2}} +\:{bx}\:+{c}\:=\:\mathrm{0} \\ $$$${a}\left(\frac{\mathrm{1}}{\mathrm{2}}{y}\right)^{\mathrm{2}}…

find-the-value-of-b-and-B-U-A-B-if-U-1-2-3-4-5-6-7-8-9-10-A-2-4-5-6-B-1-5-8-9-is-a-unoin-

Question Number 7323 by rohit meena last updated on 23/Aug/16 $${find}\:{the}\:{value}\:{of} \\ $$$$\Delta'\Lambda\:{b}\:{and}\:\left({B}'{U}\:{A}\right)\:\boldsymbol{\Lambda}\:{B} \\ $$$${if}\:{U}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\} \\ $$$${A}=\left\{\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{6}\right\} \\ $$$${B}=\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\Lambda\:{is}\:{a}\:{unoin} \\ $$ Commented by…

hi-for-a-0-1-and-n-1-a-n-1-n-k-0-n-1-a-k-n-k-prove-that-n-0-we-get-0-a-n-1-

Question Number 138383 by henderson last updated on 12/Apr/21 $$\boldsymbol{\mathrm{hi}}\:! \\ $$$$\boldsymbol{\mathrm{for}}\:{a}_{\mathrm{0}} \:=\:\mathrm{1}\:\boldsymbol{\mathrm{and}}\:\forall\:{n}\:\geqslant\:\mathrm{1},\:{a}_{{n}} \:=\:\frac{\mathrm{1}}{{n}}\:\underset{{k}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\:\frac{{a}_{{k}} }{{n}−{k}}\:. \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\forall\:{n}\:\geqslant\:\mathrm{0},\:\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{get}}\:\mathrm{0}\:\leqslant\:{a}_{{n}} \:\leqslant\:\mathrm{1}. \\ $$ Commented by mitica…