Category: Algebra

Question Number 137563 by liberty last updated on 04/Apr/21 $$let\frac{x^2+y^2}{x^2-y^2}+\frac{x^2-y^2}{x^2+y^2}=k$$$${find}\:{the}\:{value}\:{of}\:\frac{{x}^{\mathrm{8}} +{y}^{\mathrm{8}} }{{x}^{\mathrm{8}} −{y}^{\mathrm{8}} }+\frac{{x}^{\mathrm{8}} −{y}^{\mathrm{8}}…

Question Number 6476 by sanusihammed last updated on 28/Jun/16 Answered by Rasheed Soomro last updated on 28/Jun/16 $$Givenequation:x^2-px+8=0$$$$Sumoftheroots=-\frac{coefficientofx}{coefficientof{x}^2}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=−\frac{−{p}}{\mathrm{1}}={p} \…

Question Number 71960 by TawaTawa last updated on 22/Oct/19 Answered by mind is power last updated on 22/Oct/19 $$\mathrm{\Sigma }\frac{1+\mathrm{a}}{1-\mathrm{a}}=\mathrm{\Sigma }(-1+\frac{2}{1-\mathrm{a}})=\mathrm{\Sigma }-1+\mathrm{\Sigma }\frac{2}{1-\mathrm{a}}$$$$\frac{{\mathrm{p}}^{\prime }\left(\mathrm{x}\right)}{\mathrm{p}\left(\mathrm{x}\right)}=\sum _{\mathrm{a}\in \mathrm{Root}\left(\mathrm{p}\right)}\frac{1}{\mathrm{x}-\mathrm{a}}$$$$\Rightarrow\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{3}}…

Question Number 137473 by mr W last updated on 03/Apr/21 $$whatislarger?{99}^{100}or{100}^{99}?$$ Answered by MJS_new last updated on 03/Apr/21 $${n}^{{n}+\mathrm{1}} >\left({n}+\mathrm{1}\right)^{{n}} \:\forall\:{n}\geqslant\mathrm{3}…

Question Number 137472 by mr W last updated on 03/Apr/21 $$solve$$$$x^3-2\left[x\right]=5$$ Answered by MJS_new last updated on 03/Apr/21 $$\left(\mathrm{1}\right)\:\:\mathrm{1}<{x}<\mathrm{2} \…