Category: Algebra

Question Number 151179 by mathdanisur last updated on 18/Aug/21 $$\mathrm{if}\mid \mathbf{x}\mid <1$$$$\mathrm{find}\mathrm{x}+{2\mathrm{x}}^2+{3\mathrm{x}}^3+\dots$$ Answered by Olaf_Thorendsen last updated on 18/Aug/21 $$\mathrm{S}\left({x}\right)\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty}…

Question Number 85624 by Power last updated on 23/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 151142 by mathdanisur last updated on 18/Aug/21 $$\mathrm{if}\mathrm{x};\mathrm{y};\mathrm{z}\in {\mathbb{R}}^{+}\mathrm{and}\frac{1}{{\mathrm{x}}^2}+\frac{1}{{\mathrm{y}}^2}+\frac{1}{{\mathrm{z}}^2}=\frac{27}{4}$$$$\mathrm{prove}\mathrm{that}:$$$$\frac{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}}…

Question Number 20052 by Tinkutara last updated on 21/Aug/17 $$\mathrm{If}\mathrm{the}\mathrm{roots}\alpha \mathrm{and}\beta \mathrm{of}\mathrm{the}\mathrm{equation}$$$${ax}^2+bx+c=0\mathrm{are}\mathrm{real}\mathrm{and}\mathrm{of}\mathrm{opposite}$$$$\mathrm{sign}\mathrm{then}\mathrm{the}\mathrm{roots}\mathrm{of}\mathrm{the}\mathrm{equation}$$$$\alpha {(x-\beta )}^2+\beta {(x-\alpha )}^2\mathrm{is}/\mathrm{are}$$$$\left(1\right)\mathrm{Positive}$$$$\left(2\right)\mathrm{Negative}$$$$\left(\mathrm{3}\right)\:\mathrm{Real}\:\mathrm{and}\:\mathrm{opposite}\:\mathrm{sign}…

Question Number 20051 by Tinkutara last updated on 22/Aug/17 $$\mathrm{If}x\in R\mathrm{then}\frac{x^2+2x+a}{x^2+4x+3a}\mathrm{can}\mathrm{take}\mathrm{all}$$$$\mathrm{real}\mathrm{values}\mathrm{if}$$$$\left(1\right)a\in (0,2)$$$$\left(2\right)a\in [0,1]$$$$\left(3\right)a\in [-1,1]$$$$\left(4\right)\mathrm{None}\mathrm{of}\mathrm{these}$$ Answered…