Category: Algebra

Question Number 118180 by mathocean1 last updated on 15/Oct/20 $$showthatifnisodd,n(n^2+3)iseven.$$ Answered by floor(10²Eta[1]) last updated on 15/Oct/20 $$\mathrm{if}\mathrm{n}\mathrm{is}\mathrm{odd}\Rightarrow \mathrm{n}=2\mathrm{k}+1,\mathrm{k}\in \mathbb{Z}$$$$\left(\mathrm{2k}+\mathrm{1}\right)\left(\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{3}\right) \…

Question Number 118172 by I want to learn more last updated on 15/Oct/20 $$\mathrm{Find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{rhombus}\mathrm{with}\mathrm{side}8\mathrm{cm}$$ Answered by MJS_new last updated on 15/Oct/20 $$\mathrm{more}\:\mathrm{information}\:\mathrm{needed} \…

Question Number 183669 by mnjuly1970 last updated on 28/Dec/22 $$$$$$f\left(x\right)=\frac{x}{1+x+x^2}$$$${min}_f=?$$ Answered by manolex last updated on 28/Dec/22…

Question Number 52573 by Necxx last updated on 09/Jan/19 $$Findtherelationbetweenpqandr$$$$ifoneoftherootoftheequation$$$${px}^2+qx+r=0isdoubletheother.$$ Answered by mr W last updated on 09/Jan/19…

Question Number 183592 by greougoury555 last updated on 27/Dec/22 $$\{\begin{array}{l}\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{z}}+\sqrt{\frac{z}{x}}=3\\ \sqrt{\frac{y}{x}}+\sqrt{\frac{z}{y}}+\sqrt{\frac{x}{z}}=3\\ \sqrt{xyz}=1\end{array}$$$$$$$$$$ Answered by mr W last updated on 27/Dec/22 $${a}=\sqrt{\frac{{x}}{{y}}},\:{b}=\sqrt{\frac{{y}}{{z}}},\:{c}=\sqrt{\frac{{z}}{{x}}}…