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Category: Algebra

Prove-by-the-principle-of-induction-that-1-4-7-2-5-8-3-6-9-n-n-3-n-6-n-4-n-1-n-6-n-7-

Question Number 177931 by Spillover last updated on 11/Oct/22 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{the}\:\mathrm{principle}\:\mathrm{of}\: \\ $$$$\mathrm{induction}\:\mathrm{that} \\ $$$$\mathrm{1}.\mathrm{4}.\mathrm{7}+\mathrm{2}.\mathrm{5}.\mathrm{8}+\mathrm{3}.\mathrm{6}.\mathrm{9}+…\mathrm{n}\left(\mathrm{n}+\mathrm{3}\right)\left(\mathrm{n}+\mathrm{6}\right) \\ $$$$=\frac{\mathrm{n}}{\mathrm{4}}\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{6}\right)\left(\mathrm{n}+\mathrm{7}\right) \\ $$ Answered by Ar Brandon last updated on…

x-3-x-3-3-x-3-x-3-3x-

Question Number 112360 by bemath last updated on 07/Sep/20 $$\:\:\:\left(\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{x}}{\mathrm{3}}\right)^{\mathrm{3}} +\left(\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{x}}{\mathrm{3}}\right)=\:\mathrm{3x}\: \\ $$ Commented by john santu last updated on 07/Sep/20 $$\frac{\left({x}^{\mathrm{3}} +{x}\right)^{\mathrm{3}}…

solve-for-x-R-3-3-3-3-3-x-x-

Question Number 177873 by mr W last updated on 10/Oct/22 $${solve}\:{for}\:{x}\in\mathbb{R} \\ $$$$\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+\sqrt{\mathrm{3}+{x}}}}}}={x} \\ $$ Answered by Frix last updated on 10/Oct/22 $$\mathrm{for}\:\mathrm{given}\:{a}\geqslant\mathrm{0}\:\mathrm{we}\:\mathrm{need}\:{x}\:\mathrm{so}\:\mathrm{that} \\ $$$$\sqrt{{a}+{x}}={x}\:\Rightarrow\:{x}=\frac{\mathrm{1}+\sqrt{\mathrm{4}{a}+\mathrm{1}}}{\mathrm{2}}…

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

Question Number 177856 by mathlove last updated on 10/Oct/22 $${p}\left({x}\right)+{p}\left({x}−\mathrm{1}\right)=\mathrm{2}{x}+\mathrm{4} \\ $$$${p}\left({x}\right)=? \\ $$ Answered by blackmamba last updated on 10/Oct/22 $$\:\:{p}\left({x}\right)={ax}+{b}\: \\ $$$$\:\:{p}\left({x}−\mathrm{1}\right)={a}\left({x}−\mathrm{1}\right)+{b}={ax}+{b}−{a} \\…

Solve-the-system-x-y-z-30-equation-i-x-3-y-2-2z-30-equation-ii-

Question Number 46785 by Tawa1 last updated on 31/Oct/18 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{30}\:\:\:\:\:\:\:\:\:…..\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{x}}{\mathrm{3}}\:+\:\frac{\mathrm{y}}{\mathrm{2}}\:+\:\mathrm{2z}\:\:=\:\:\mathrm{30}\:\:\:\:\:……\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered by MJS last updated on 31/Oct/18…