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Category: Algebra

Find-square-root-of-7-30-2-i-

Question Number 27681 by ajfour last updated on 12/Jan/18 $${Find}\:{square}\:{root}\:{of}\:\mathrm{7}−\mathrm{30}\sqrt{\mathrm{2}}{i}\:. \\ $$ Commented by Rasheed.Sindhi last updated on 13/Jan/18 $$\mathrm{Squareroot}\:\mathrm{of}\:\mathrm{7}−\mathrm{30}\sqrt{\mathrm{2}}{i}\:? \\ $$$$\mathrm{Let}\:\pm\sqrt{\mathrm{7}−\mathrm{30}\sqrt{\mathrm{2}}\:\mathrm{i}}=\mathrm{p}+\mathrm{q}\sqrt{\mathrm{2}}\:\mathrm{i} \\ $$$$\mathrm{where}\:\mathrm{p},\mathrm{q}\in\mathbb{Q} \\…

Find-0-1-x-2-x-1-1-ax-dx-a-gt-0-

Question Number 158721 by HongKing last updated on 08/Nov/21 $$\mathrm{Find}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{1}\:+\:\mathrm{ax}\right)}\:\mathrm{dx}\:\:;\:\:\mathrm{a}>\mathrm{0} \\ $$$$ \\ $$ Answered by ajfour last updated on…

let-a-gt-b-gt-c-gt-0-solve-in-R-ax-by-cz-a-bx-cy-az-b-cx-ay-bz-c-

Question Number 158724 by HongKing last updated on 08/Nov/21 $$\mathrm{let}\:\:\mathrm{a}>\mathrm{b}>\mathrm{c}>\mathrm{0}\:\:\mathrm{solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\begin{cases}{\mathrm{ax}\:+\:\mathrm{by}\:+\:\mathrm{cz}\:=\:\mathrm{a}}\\{\mathrm{bx}\:+\:\mathrm{cy}\:+\:\mathrm{az}\:=\:\mathrm{b}}\\{\mathrm{cx}\:+\:\mathrm{ay}\:+\:\mathrm{bz}\:=\:\mathrm{c}}\end{cases} \\ $$$$ \\ $$ Answered by ajfour last updated on 08/Nov/21 $${x}+{y}+{z}=\mathrm{1} \\…

If-a-n-3-a-n-1-a-n-1-and-a-0-1-a-2-2-find-a-n-

Question Number 93173 by I want to learn more last updated on 11/May/20 $$\mathrm{If}\:\:\:\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{3}} \:\:=\:\:\frac{\mathrm{a}_{\mathrm{n}\:\:−\:\:\mathrm{1}} }{\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{1}} }\:,\:\:\:\:\mathrm{and}\:\:\:\mathrm{a}_{\mathrm{0}} \:\:=\:\:\mathrm{1},\:\:\:\mathrm{a}_{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\mathrm{find}\:\:\:\mathrm{a}_{\mathrm{n}} \\ $$ Answered by…