Category: Algebra

Question Number 63021 by kaivan.ahmadi last updated on 27/Jun/19 $$solvethisequation$$$$$$$$x^y=y^x$$$$$$$$$$$$x,y\in \mathbb{R}.$$ Commented by…

Question Number 128508 by Lian last updated on 08/Jan/21 $$if{x}^{x^3}=3$$$$findx$$ Answered by mr W last updated on 08/Jan/21 $${if}\:{x}^{\mathrm{3}}…

Question Number 62945 by Tawa1 last updated on 27/Jun/19 $$\mathrm{Find}\mathrm{the}\mathrm{greatest}\mathrm{coefficient}\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{of}{(6-4\mathrm{x})}^{-3}$$ Answered by mr W last updated on 27/Jun/19 $${(6-4x)}^{-3}$$$$=\mathrm{6}^{−\mathrm{3}} \left(\mathrm{1}−\frac{\mathrm{2}{x}}{\mathrm{3}}\right)^{−\mathrm{3}} \…

Question Number 128458 by SLVR last updated on 07/Jan/21 Commented by BHOOPENDRA last updated on 07/Jan/21 $$Givenf\left(f\left(1\right)\right)=0,f\left(f\left(2\right)\right)=0$$$$i.eequationf\left(x\right)=0$$$$hastworootf\left(1\right)andf\left(2\right)$$$$f\left(1\right)+f\left(2\right)=-\alpha andf\left(1\right).f\left(2\right)=\beta$$$${so}\:\mathrm{5}+\mathrm{3}\alpha+\mathrm{2}\beta=−\alpha…

Question Number 128457 by SLVR last updated on 07/Jan/21 Commented by BHOOPENDRA last updated on 07/Jan/21 $$x^5=\frac{133x-78}{133-78x}$$$$78x^6-133x^5+133-78=0$$$$\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{78}{x}^{\mathrm{4}}…