Category: Algebra

Question Number 164039 by ArielVyny last updated on 13/Jan/22 $$considerffunctionDf=[0,1]$$$$f\left(0\right)=f\left(1\right)c\in [0,\frac{1}{2}]showthatf\left(c\right)=f(c+\frac{1}{2})$$ Answered by Ar Brandon last updated on 13/Jan/22 $$f\left(0\right)=f\left(1\right)$$$${f}\left({c}+\mathrm{0}\right)={f}\left({c}+\mathrm{1}\right)\:,\:\mathrm{since}\:{f}\:<\:\mathrm{1}-\mathrm{periodic}…

Question Number 164024 by mathlove last updated on 13/Jan/22 Answered by som(math1967) last updated on 13/Jan/22 $$x^2-y^2=-(x-y)$$$$(x-y)(x+y)+(x-y)=0$$$$(x-y)(x+y+1)=0$$$${x}+{y}=−\mathrm{1}\:\left[{x}\neq{y}\right]…

Question Number 164019 by ajfour last updated on 13/Jan/22 $$x^4+{ax}^3+{bx}^2+cx+d=0$$$$\Rightarrow x^2+\frac{d}{x^2}+ax+\frac{c}{x}+b=0$$$$say\frac{1}{x}=t\Rightarrow$$$$x^2+ax+b+{dt}^2+ct=0$$$${let}\:\:\:\:{x}^{\mathrm{2}}…

Question Number 164001 by bekzodjumayev last updated on 12/Jan/22 Commented by bekzodjumayev last updated on 12/Jan/22 $$Help$$ Answered by mahdipoor last updated on…

Question Number 98448 by Quvonchbek last updated on 14/Jun/20 $$6^{273}+8^{273}:49\mathit{p}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathbf{s}\mathit{i}\mathit{o}\mathit{n}$$ Commented by Rasheed.Sindhi last updated on 14/Jun/20 $$\:\:\:\:\:\:\mathrm{49}\:\mid\:\mathrm{2}^{\mathrm{273}} \left(\mathrm{3}^{\mathrm{273}} +\mathrm{4}^{\mathrm{273}} \right)…