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Category: Algebra

Question-98859

Question Number 98859 by peter frank last updated on 16/Jun/20 Commented by mr W last updated on 16/Jun/20 $${p}\left({x}\right)={q}\left({x}\right)\left({x}−\mathrm{1}\right) \\ $$$${p}\left(\mathrm{1}\right)=\mathrm{0} \\ $$$$\mathrm{1}+{c}−\mathrm{2}{c}+\mathrm{4}=\mathrm{0} \\ $$$$\Rightarrow{c}=\mathrm{5}…

let-f-x-be-a-dolvnomial-of-degree-4-such-that-f-1-1-f-2-2-f-3-3-f-4-4-then-f-6-

Question Number 98842 by  M±th+et+s last updated on 16/Jun/20 $${let}\:{f}\left({x}\right)\:{be}\:{a}\:{dolvnomial}\:{of}\:{degree}\:\mathrm{4}\: \\ $$$${such}\:{that}\:{f}\left(\mathrm{1}\right)=\mathrm{1}\:,\:{f}\left(\mathrm{2}\right)=\mathrm{2}\:,{f}\left(\mathrm{3}\right)=\mathrm{3},{f}\left(\mathrm{4}\right)=\mathrm{4} \\ $$$${then}\:{f}\left(\mathrm{6}\right)=? \\ $$ Commented by mr W last updated on 16/Jun/20 $${see}\:{also}\:{Q}\mathrm{98268}…

Please-explain-1-i-lt-j-n-ij-j-2-n-j-j-1-j-2-I-want-to-know-how-L-H-S-R-H-S-

Question Number 98844 by I want to learn more last updated on 16/Jun/20 $$\mathrm{Please}\:\mathrm{explain}:\:\:\:\:\:\:\underset{\mathrm{1}\:\leqslant\:\boldsymbol{\mathrm{i}}\:<\:\boldsymbol{\mathrm{j}}\:\leqslant\:\boldsymbol{\mathrm{n}}} {\sum}\boldsymbol{\mathrm{ij}}\:\:\:\:=\:\:\:\underset{\boldsymbol{\mathrm{j}}\:\:=\:\:\mathrm{2}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\frac{\boldsymbol{\mathrm{j}}\left(\boldsymbol{\mathrm{j}}\:−\:\mathrm{1}\right)\boldsymbol{\mathrm{j}}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{I}}\:\mathrm{want}\:\mathrm{to}\:\mathrm{know}\:\mathrm{how}\:\mathrm{L}.\mathrm{H}.\mathrm{S}\:\:=\:\:\mathrm{R}.\mathrm{H}.\mathrm{S} \\ $$ Answered by mr W…

x-4-x-2-cx-x-2-1-2-2-cx-1-4-let-x-2-1-2-t-t-2-1-4-2-c-2-t-1-2-now-let-t-2-1-4-z-z-2-c-2-2-2-c-4-z-1-4-z-2-c-2-2-p-p-2-c-4-4-2-c-8-p

Question Number 164341 by ajfour last updated on 16/Jan/22 $$\:\:{x}^{\mathrm{4}} ={x}^{\mathrm{2}} +{cx} \\ $$$$\left({x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} ={cx}+\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${let}\:\:\:\:{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}={t}\:\:\:\Rightarrow \\ $$$$\left({t}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} ={c}^{\mathrm{2}} \left({t}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\…