Category: Algebra

Question Number 8148 by Rasheed Soomro last updated on 02/Oct/16 $$\mathrm{Determine}{\mathrm{x}}^4-\frac{1}{{\mathrm{x}}^4},\mathrm{if}{\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}=34.$$ Commented by sou1618 last updated on 02/Oct/16 $${set}\:{X}={x}^{\mathrm{2}}…

Question Number 8134 by 314159 last updated on 01/Oct/16 Answered by prakash jain last updated on 01/Oct/16 $$\mathrm{See}\mathrm{question}8025.$$ Terms of Service Privacy Policy…

Question Number 139193 by EnterUsername last updated on 23/Apr/21 $$\underset{m=1}{\sum ^{32}}(3m+2){\left(\underset{n=1}{\sum ^{10}}(\sin \left(\frac{2n\pi }{11}\right)-\mathrm{icos}\left(\frac{2n\pi }{11}\right))\right)}^m=$$$$\left(\mathrm{A}\right)4(1-i)\left(\mathrm{B}\right)12(1+i)$$$$\left(\mathrm{C}\right)12(1-i)\left(\mathrm{D}\right)48(1-i)$$ Answered by qaz last…

Question Number 139192 by EnterUsername last updated on 23/Apr/21 $$\mathrm{If}{z}_1\mathrm{and}{z}_2\mathrm{are}\mathrm{complex}n\mathrm{th}\mathrm{roots}\mathrm{of}\mathrm{unity}\mathrm{which}\mathrm{sub}-$$$$\mathrm{tend}\mathrm{right}\mathrm{angle}\mathrm{at}\mathrm{the}\mathrm{origin},\mathrm{then}n\mathrm{must}\mathrm{be}\mathrm{of}\mathrm{the}\mathrm{form}$$$$\left(\mathrm{A}\right)4\mathrm{K}+1\left(\mathrm{B}\right)4\mathrm{K}+2$$$$\left(\mathrm{C}\right)4\mathrm{K}+3\left(\mathrm{D}\right)4\mathrm{K}$$ Answered by mr W last…

Question Number 139165 by mathlove last updated on 23/Apr/21 Answered by mr W last updated on 23/Apr/21 $$13+\sqrt{48}={\left(2\sqrt{3}\right)}^2+2\times 2\sqrt{3}+1={(2\sqrt{3}+1)}^2$$$$5-\sqrt{13+\sqrt{48}}=5-(2\sqrt{3}+1)={\left(\sqrt{3}\right)}^2-2\sqrt{3}+1={(\sqrt{3}-1)}^2$$$$\mathrm{3}+\sqrt{\mathrm{5}−\sqrt{\mathrm{13}+\sqrt{\mathrm{48}}}}=\mathrm{3}+\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)=\mathrm{2}+\sqrt{\mathrm{3}} \…