Category: Algebra

Question Number 188226 by Shrinava last updated on 26/Feb/23 $$\mathrm{If}\mathrm{\Omega }=\sum _{\mathbf{cyc}}\frac{\sin (\mathrm{A}-\frac{\pi }{6})}{\cos (\mathrm{B}-\frac{\pi }{6})\cos (\mathrm{C}-\frac{\pi }{6})}\mathrm{in}△\mathrm{ABC}$$$$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$${\mathrm{x}}^4-4\mathrm{\Omega }{\mathrm{x}}^3+6\mathrm{\Omega }{\mathrm{x}}^2-4\mathrm{\Omega }\mathrm{x}+1=0$$ Answered by aleks041103 last updated…

Question Number 122658 by mathocean1 last updated on 18/Nov/20 $$wearein{\mathbb{C}}^3.$$$$\left(S\right):\{\begin{array}{l}x+y+z=2i-1andxyz=2\\ xy+yz+xz=-2(1+i)\end{array}$$$$P\left(z\right)=z^3+(1-2i)z^2-2(1+i)-2.$$$$showthat(a,b,c)issolution$$$$of\left(S\right)ifandonlya;b;care$$$$rootsofP.$$…

Question Number 122651 by mathocean1 last updated on 18/Nov/20 $$showthatif$$$$5^{3n}+5^{2n}+5^n+1isdivisibleby$$$$13,thenn(\in \mathbb{N})isnota$$$$multipleof4.$$ Answered by mindispower last…

Question Number 122648 by mathocean1 last updated on 18/Nov/20 $$Determinatethevaluesofn\in \mathbb{N}$$$$suchthatn-1candivise2n+3$$ Answered by TANMAY PANACEA last updated on 18/Nov/20 $$2n-2+5whendevidedbyn-1$$$$\mathrm{2}+\frac{\mathrm{5}}{{n}−\mathrm{1}}\:\:\:\:\:{n}\:{should}\:{be}\:\mathrm{6}…

Question Number 122647 by mathocean1 last updated on 18/Nov/20 $$p\in \mathbb{Z}.given:$$$$u=14p+3;v=5p+1,$$$$\left(E\right):87x+31y=2;wehave$$$$alsotheline\left(D\right):87x-31y=2$$$$1)showthatuandvareprimes$$$$betweenthem.(imeanthe$$$${don}^{\prime }thaveanycommondivisor$$$$\left.{excepted}\:\mathrm{1}\:{and}\:−\mathrm{1}.\right) \…