Category: Algebra

Question Number 25457 by Tinkutara last updated on 10/Dec/17 Answered by prakash jain last updated on 10/Dec/17 $$n^2+n+1=an(n-1)+bn+c$$$$n(n-1)+2n+1$$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{i}}…

Question Number 25444 by math solver last updated on 10/Dec/17 Commented by Rasheed.Sindhi last updated on 16/Dec/17 $$\overline{\mathrm{z}}+1={\mathrm{iz}}^2+\mid \mathrm{z}{\mid }^2$$$$\mathrm{z}=\mathrm{x}+\mathrm{iy}\Rightarrow\overline {\mathrm{x}+\mathrm{iy}}+\mathrm{1}=\mathrm{i}\left(\mathrm{x}+\mathrm{iy}\right)^{\mathrm{2}} +\mid\mathrm{x}+\mathrm{iy}\mid \…

Question Number 156502 by MathSh last updated on 11/Oct/21 $$\mathrm{Solve}\mathrm{for}\mathrm{integers}:$$$$({\mathrm{x}}^2+{\mathrm{y}}^2)({\mathrm{x}}^4+{\mathrm{y}}^4)={(\mathrm{x}+\mathrm{y})}^6$$$$$$ Answered by Rasheed.Sindhi last updated…

Question Number 156485 by MathSh last updated on 11/Oct/21 $$2021!\underset{\mathbf{n}=0}{\sum ^{\mathrm{\infty }}}\underset{\mathbf{k}=0}{\sum ^{\mathrm{\infty }}}\frac{1}{\underset{\mathbf{m}=1}{\prod ^{2022}}(\mathrm{n}+\mathrm{k}+\mathrm{m})}=\frac{1}{\mathrm{A}}$$$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathbf{A}$$ Terms of Service Privacy Policy…

Question Number 156482 by MathSh last updated on 11/Oct/21 $$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$$3+\sin \left(2\mathrm{x}\right)=4\sin (\mathrm{x}+\frac{\pi }{4})$$ Answered by mr W last updated on 11/Oct/21 $$3+\sin \left(2x\right)=2\sqrt{2}(\sin x+\cos x)$$$$\mathrm{9}+\mathrm{6sin}\:\left(\mathrm{2}{x}\right)+\mathrm{sin}^{\mathrm{2}}…