Category: Algebra

Question Number 56183 by 121194 last updated on 11/Mar/19 $$\mathrm{find}\mathrm{all}a,b\in \mathbb{R}\mathrm{such}\mathrm{that}$$$$\frac{1}{a+bi}=\frac{1}{a}+\frac{i}{b}$$ Answered by kaivan.ahmadi last updated on 11/Mar/19 $$\frac{\mathrm{1}}{{a}+{bi}}=\frac{{b}+{ai}}{{ab}}\Rightarrow{ab}+\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right){i}−{ab}={ab}\Rightarrow \…

Question Number 187254 by mnjuly1970 last updated on 15/Feb/23 Answered by MJS_new last updated on 15/Feb/23 $$c=a+b\Rightarrow E=\frac{2{(a^2+ab+b^2)}^2}{ab}>0$$ Terms of Service…

Question Number 56179 by problem solverd last updated on 11/Mar/19 $$\mathrm{draw}\mathrm{the}\mathrm{graph}\mathrm{of}$$$$\mathrm{f}\left(x\right)=\sqrt{1-x^2}$$$$\mathrm{for}0⩽x⩽1$$ Commented by mr W last updated on…

Question Number 187233 by ajfour last updated on 15/Feb/23 $$Findxif:x^4+a=x\mathrm{\forall }(0<a<\frac{2}{9})$$ Commented by MJS_new last updated on 15/Feb/23 $$\mathrm{maybe}\mathrm{off}\mathrm{topic}\mathrm{but}\mathrm{it}\mathrm{could}\mathrm{be}\mathrm{of}\mathrm{interest}$$$$\left({x}−\frac{{p}^{\mathrm{2}} }{\mathrm{2}}−\frac{\sqrt{\mathrm{2}−{p}^{\mathrm{6}} }}{\mathrm{2}{p}}\right)\left({x}−\frac{{p}^{\mathrm{2}}…

Question Number 121684 by mathocean1 last updated on 10/Nov/20 $$\theta \in [0;2\pi ].$$$$solvein\mathbb{C}thisequation:$$$$z^2-\left(2^{\theta +1}cos\theta \right)z+2^{2\theta }=0$$$$$$ Commented by Dwaipayan Shikari…