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arg-z-a-arg-z-z-1-arg-z-z-1-kpi-a-R-z-1-C-z-1-0-z-C-k-Z-the-locus-of-z-are-

Question Number 651 by 123456 last updated on 19/Feb/15 $$\mathrm{arg}\left(\mathrm{z}−\mathrm{a}\right)−\mathrm{arg}\left(\mathrm{z}−\mathrm{z}_{\mathrm{1}} \right)−\mathrm{arg}\left(\mathrm{z}−\bar {\mathrm{z}}_{\mathrm{1}} \right)={k}\pi \\ $$$${a}\in\mathbb{R} \\ $$$${z}_{\mathrm{1}} \in\mathbb{C},\Im\left(\bar {{z}}_{\mathrm{1}} \right)\neq\mathrm{0} \\ $$$${z}\in\mathbb{C} \\ $$$${k}\in\mathbb{Z} \\…

Evaluate-x-x-1-dx-

Question Number 66548 by AnjanDey last updated on 17/Aug/19 $$\boldsymbol{{Evaluate}}:\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}\:}{dx} \\ $$ Commented by AnjanDey last updated on 19/Aug/19 $${Please}\:{evaluate}\:{this}\:{integral}…{It}'{s}\:{very}\:{needful}\:{and}\:{urgent}… \\ $$ Terms of Service…

3-3x-4-3-x-2-4-

Question Number 991 by Madan pd gupta last updated on 13/May/15 $$\mathrm{3}\left(\mathrm{3}{x}−\mathrm{4}\right)+\mathrm{3}\left({x}−\mathrm{2}\right)=\mathrm{4} \\ $$ Answered by prakash jain last updated on 13/May/15 $$\mathrm{9}{x}−\mathrm{12}+\mathrm{3}{x}−\mathrm{6}=\mathrm{0} \\ $$$$\mathrm{12}{x}=\mathrm{18}\Rightarrow{x}=\frac{\mathrm{18}}{\mathrm{12}}=\frac{\mathrm{3}}{\mathrm{2}}…

tan-x-tan-y-z-a-tan-y-tan-z-x-b-tan-z-tan-x-y-c-for-wich-values-of-a-b-c-the-system-have-solutions-x-y-z-a-b-c-R-6-

Question Number 976 by 123456 last updated on 11/May/15 $$\begin{cases}{\mathrm{tan}\:{x}\:\mathrm{tan}\:\left({y}−{z}\right)={a}}\\{\mathrm{tan}\:{y}\:\mathrm{tan}\:\left({z}−{x}\right)={b}}\\{\mathrm{tan}\:{z}\:\mathrm{tan}\:\left({x}−{y}\right)={c}}\end{cases} \\ $$$$\mathrm{for}\:\mathrm{wich}\:\mathrm{values}\:\mathrm{of}\:{a},{b},{c}\:\mathrm{the}\:\mathrm{system} \\ $$$$\mathrm{have}\:\mathrm{solutions}? \\ $$$$\left({x},{y},{z},{a},{b},{c}\right)\in\mathbb{R}^{\mathrm{6}} \\ $$ Commented by 123456 last updated on 11/May/15…