Question Number 8661 by FilupSmith last updated on 20/Oct/16 $${p}_{{n}} ={n}^{{th}} \:\mathrm{prime}\:\mathrm{number} \\ $$$${p}_{\mathrm{1}} =\mathrm{2},\:{p}_{\mathrm{2}} =\mathrm{3},\:{p}_{\mathrm{3}} =\:\mathrm{5},\:… \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{following}\:\mathrm{converge}: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{p}_{{i}}…
Question Number 8644 by prakash jain last updated on 19/Oct/16 $$\mathrm{Write}\:\mathrm{an}\:\mathrm{expression}\:\mathrm{involving} \\ $$$${e}\:\mathrm{and}\:\pi\:\mathrm{which}\:\mathrm{when}\:\mathrm{evaluated} \\ $$$$\mathrm{gives}\:\mathrm{result}\:\mathrm{1}. \\ $$ Commented by Yozzias last updated on 19/Oct/16 $$\mathrm{ee}^{−\mathrm{1}}…
Question Number 74168 by mr W last updated on 19/Nov/19 Commented by mr W last updated on 19/Nov/19 $${solve}\:{for}\:{x}. \\ $$ Answered by Rio Michael…
Question Number 8635 by tawakalitu last updated on 19/Oct/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{5}^{\sqrt{\mathrm{x}}} \:−\:\mathrm{5}^{\mathrm{x}} \:−\:\mathrm{7}\:=\:\mathrm{100} \\ $$ Answered by ridwan balatif last updated on 19/Oct/16 $$\mathrm{5}^{\sqrt{\mathrm{x}}}…
Question Number 8633 by Yozzias last updated on 19/Oct/16 $$\mathrm{Find}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{n}^{\mathrm{p}} }{\mathrm{x}^{\mathrm{n}} }\:\:\:\mathrm{where}\:\mathrm{p}\in\mathbb{Z}^{+} . \\ $$ Commented by prakash jain last updated on 19/Oct/16 $$\mathrm{Does}\:{x}\:\mathrm{cover}\:\mathrm{entire}\:\mathrm{range}\:\mathrm{of}\:\mathbb{R}?…
Question Number 74164 by MASANJAJ last updated on 19/Nov/19 $${factorize} \\ $$$$\mathrm{6}{x}^{\mathrm{2}} \:−\mathrm{11}{xy}\:−\mathrm{10}{y}^{\mathrm{2}} \\ $$ Answered by MJS last updated on 19/Nov/19 $$\mathrm{6}{x}^{\mathrm{2}} −\mathrm{11}{xy}−\mathrm{10}{y}^{\mathrm{2}} =\mathrm{0}…
Question Number 139700 by EnterUsername last updated on 30/Apr/21 $$\mathrm{If}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{distinct}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mid{z}_{\mathrm{1}} \mid=\mid{z}_{\mathrm{2}} \mid=\mid{z}_{\mathrm{3}} \mid=\mathrm{1}\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{z}_{\mathrm{1}} ^{\mathrm{2}} }{{z}_{\mathrm{2}} {z}_{\mathrm{3}} }+\frac{{z}_{\mathrm{2}} ^{\mathrm{2}}…
Question Number 139695 by john_santu last updated on 30/Apr/21 $$\:\mid{x}^{\mathrm{2}} −\mathrm{4}{x}\mid\:+\mid{x}\mid\:\geqslant\:\mathrm{3}\: \\ $$ Answered by MJS_new last updated on 30/Apr/21 $$\mid{x}\left({x}−\mathrm{4}\right)\mid+\mid{x}\mid=\mathrm{3} \\ $$$$\mathrm{squaring} \\ $$$${x}^{\mathrm{2}}…
Question Number 74148 by mathocean1 last updated on 19/Nov/19 $$\begin{cases}{−{x}\sqrt{\mathrm{3}}+\mathrm{2}{my}\sqrt{\mathrm{2}}=\frac{\sqrt{\mathrm{3}}}{\mathrm{3}}}\\{\mathrm{2}{mx}−\mathrm{3}{y}\sqrt{\mathrm{6}}=\mathrm{1}}\end{cases}\:\:\:\:\:\: \\ $$$$ \\ $$$${help}\:{me}\:{solve}\:{it}. \\ $$ Answered by MJS last updated on 19/Nov/19 $$\mathrm{2}\:\mathrm{equations}\:\mathrm{in}\:\mathrm{3}\:\mathrm{unknowns}\:\Rightarrow\:\mathrm{parametric} \\…
Question Number 139672 by mathlove last updated on 30/Apr/21 Answered by MJS_new last updated on 30/Apr/21 $$\left({x}^{{a}} \right)^{{b}} ={x}^{{ab}} \\ $$$$\left({x}^{{a}} \right)^{{a}} ={x}^{{a}^{\mathrm{2}} } \\…