Category: Algebra

Question Number 191553 by MATHEMATICSAM last updated on 25/Apr/23 $$\mathrm{If}{a}^2+a+1=0\mathrm{then}\mathrm{find}{a}^5+a^4+1.$$ Commented by Tinku Tara last updated on 25/Apr/23 $${a}=\omega,\:\omega^{\mathrm{2}} ,\:\mathrm{where}\:\omega\:\mathrm{is}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity}.…

Question Number 191552 by MATHEMATICSAM last updated on 25/Apr/23 $$\mathrm{If}{x}^2-3x+1=0\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}$$$${(x^2+x+\frac{1}{x}+\frac{1}{x^2})}^2$$ Answered by mr W last updated on 25/Apr/23…

Question Number 191546 by MATHEMATICSAM last updated on 25/Apr/23 $$\mathrm{If}m+1=\sqrt{n}+3\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}$$$$\frac{1}{2}(\frac{m^3-6m^2+12m-8}{\sqrt{n}}-n)$$ Answered by som(math1967) last updated on 25/Apr/23 $$\frac{\mathrm{1}}{\mathrm{2}}×\left\{\frac{\left({m}−\mathrm{2}\right)^{\mathrm{3}} }{\:\sqrt{{n}}}\:−{n}\right\}…

Question Number 191529 by MATHEMATICSAM last updated on 25/Apr/23 $$\mathrm{If}\frac{x-y}{x\sqrt{y}+y\sqrt{x}}=\frac{1}{\sqrt{x}};(x>0\mathrm{and}y>0)\mathrm{then}$$$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\frac{x}{y}.$$ Answered by mehdee42 last updated on 25/Apr/23 $$\frac{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}{\sqrt{xy}(\sqrt{x}+\sqrt{y})}=\frac{1}{\sqrt{x}}$$$${x}−\sqrt{{xy}}=\sqrt{{xy}}\Rightarrow{x}=\mathrm{2}\sqrt{{xy}}\Rightarrow\frac{{x}}{{y}}=\mathrm{4}\:\checkmark \…

Question Number 191525 by mehdee42 last updated on 25/Apr/23 $$Q:Showthatthenumbers\sqrt{3},2\mathrm{\&}\sqrt{8}cannotbetermsofanarithmeticsequence.$$ Answered by mr W last updated on 26/Apr/23 $$\sqrt{3}<2<\sqrt{8}$$$$assumetheyaretermsofanA.P.,$$$${then}\:{we}\:{have}…