Question Number 110285 by mathdave last updated on 28/Aug/20 Answered by 1549442205PVT last updated on 29/Aug/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{x}^{\mathrm{8}} +\mathrm{4}=\left(\mathrm{x}^{\mathrm{4}} +\mathrm{2}\right)^{\mathrm{2}} −\mathrm{2x}^{\mathrm{4}} = \\ $$$$\left(\mathrm{x}^{\mathrm{4}} +\sqrt{\mathrm{2}}\:\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{4}}…
Question Number 175806 by Ml last updated on 07/Sep/22 Answered by cortano1 last updated on 07/Sep/22 $$\:\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{1}}\:=\:\frac{\sqrt{\mathrm{x}}\:\left(\sqrt{\mathrm{x}+\mathrm{1}}\:+\mathrm{1}\right)}{\mathrm{x}} \\ $$$$\:=\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}\:+\mathrm{1}}{\:\sqrt{\mathrm{x}}}\: \\ $$$$\:\mathrm{let}\:\sqrt{\mathrm{x}}\:=\mathrm{tan}\:\mathrm{u}\Rightarrow\mathrm{x}=\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{u}\right) \\ $$$$\:\begin{cases}{\mathrm{x}=\mathrm{1}\Rightarrow\mathrm{u}=\frac{\pi}{\mathrm{4}}}\\{\mathrm{x}=\mathrm{3}\Rightarrow\mathrm{u}=\frac{\pi}{\mathrm{3}}}\end{cases} \\…
Question Number 110254 by ZiYangLee last updated on 28/Aug/20 $$\mathrm{Given}\:\mathrm{tan}\:\alpha\:\mathrm{and}\:\mathrm{tan}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{two}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{2}{x}^{\mathrm{2}} −{x}−\mathrm{2}=\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{sin}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)+\mathrm{cos}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)+\mathrm{tan}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)=? \\ $$ Answered by som(math1967) last updated on 28/Aug/20 $$\mathrm{tan}\alpha+\mathrm{tan}\beta=\frac{\mathrm{1}}{\mathrm{2}}…
Question Number 175785 by otchereabdullai@gmail.com last updated on 06/Sep/22 Commented by Ar Brandon last updated on 07/Sep/22 #include <stdio.h> #include <math.h> int main(void) { double fx, gx, xn, x_m; printf("Enter initial value:"); scanf("%lf", &xn); for(int i=0; i<100; i++) { fx = pow(xn, log(2)/log(3))-sqrt(xn)-1; gx = log(2)/log(3)*pow(xn,log(2)/log(3)-1) -0.5/sqrt(xn); x_m = xn - fx / gx; xn = x_m; } printf("x ≈ %.2f\n", xn); return 0; } Commented by Ar Brandon last updated on…
Question Number 110227 by mohammad17 last updated on 27/Aug/20 Commented by mohammad17 last updated on 27/Aug/20 $${help}\:{me}\:{sir} \\ $$ Answered by bobhans last updated on…
Question Number 110222 by mathdave last updated on 28/Aug/20 $${find}\:{the}\:{series} \\ $$$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left[\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{3}{n}−\mathrm{2}}\right] \\ $$ Answered by mnjuly1970 last updated on 27/Aug/20 $${find}\:{the}\:{series}…
Question Number 110223 by mohammad17 last updated on 27/Aug/20 $${let}\::{A},{B},{C},{D}\:{be}\:{anone}\:{empety}\:{set}\:{prove}\:{that}\: \\ $$$${A}×{B}={C}×{D}\leftrightarrow{A}={C}\wedge{B}={D}\:? \\ $$$${help}\:{me}\:{sir} \\ $$ Commented by kaivan.ahmadi last updated on 27/Aug/20 $${I}\:{think}\:{it}\:{isnt}\:{true},\:{because}\:{in}\:{set}\:{theory}\:{we} \\…
Question Number 110214 by mathdave last updated on 27/Aug/20 $${show}\:{that}\: \\ $$$$\int_{−\infty} ^{+\infty} \frac{\left(\mathrm{1}+\frac{{x}}{\pi}\right)\mathrm{sin}\left(\pi{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{5}}{dx}=\frac{\mathrm{1}}{{e}^{\pi} } \\ $$ Answered by mathmax by abdo last updated…
Question Number 110204 by Algoritm last updated on 27/Aug/20 Commented by Algoritm last updated on 27/Aug/20 $$\blacklozenge\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:! \\ $$ Commented by prakash jain last updated…
Question Number 175740 by daus last updated on 06/Sep/22 Answered by Ar Brandon last updated on 06/Sep/22 $${S}\left({t}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{t}^{{n}} =\frac{{t}}{\mathrm{1}−{t}}\:,\:\mid{t}\mid<\mathrm{1} \\ $$$$\Rightarrow{S}\:'\left({t}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{nt}^{{n}−\mathrm{1}}…