Category: Algebra

Question Number 163651 by mathlove last updated on 09/Jan/22 $$if{(a-2b)}^2+{(b-2c)}^2=0$$$$findvolve\frac{{(b+c-a)}^3}{abc}=?$$ Commented by cortano1 last updated on 09/Jan/22 $$\left.$$\begin{array}{c}a=2b\Rightarrow b=\frac{1}{2}a\\ b=2c\Rightarrow c=\frac{1}{4}a\end{array}$$\right\}\:\Rightarrow\frac{−\frac{\mathrm{1}}{\mathrm{64}}{a}^{\mathrm{3}}…

Question Number 163632 by HongKing last updated on 08/Jan/22 $$\frac{({\mathrm{x}}^2-{\mathrm{y}}^2)\cdot \sqrt{3}}{\sqrt{{\mathrm{x}}^3+{3\mathrm{x}}^2\mathrm{y}+{3\mathrm{xy}}^2+{\mathrm{y}}^3}}=-1$$$${\mathrm{x}}^3+{\mathrm{y}}^3={(\mathrm{x}+\mathrm{y})}^2$$$$\mathrm{find}:\mathbf{x}\mathrm{and}\mathbf{y}$$ Answered…

Question Number 163631 by HongKing last updated on 08/Jan/22 $$\mathrm{x}+\frac{1}{\mathrm{x}}=\sqrt{3}\Rightarrow {\mathrm{x}}^{3579}+\frac{1}{{\mathrm{x}}^{3579}}=?$$ Answered by MathsFan last updated on 09/Jan/22 $${\mathrm{x}}^2-\mathrm{x}\sqrt{3}+1=0\to \mathrm{x}=\frac{i\pm \sqrt{3}}{2}$$$$\left(\frac{{i}\pm\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{3579}}…

Question Number 32543 by rahul 19 last updated on 27/Mar/18 $$\mathit{T}hecoefficientof{x}^{4}intheexpansion$$$$of(1+5x+9x^2+\dots ..\mathrm{\infty }){(1+x^2)}^{11}is$$$$a)171$$$$b)172$$$$c)173$$$$\left.{d}\right)\:\mathrm{176}…

Question Number 98073 by bobhans last updated on 11/Jun/20 $$\mathrm{solve}\sqrt{6-\mathrm{x}}=6-{\mathrm{x}}^2$$ Commented by john santu last updated on 11/Jun/20 $$\mathrm{equation}\mathrm{defined}\mathrm{in}6-\mathrm{x}⩾0\wedge 6-{\mathrm{x}}^2⩾0$$$$\Leftrightarrow\:\mathrm{x}\:\leqslant\:\mathrm{6}\:\wedge\:−\sqrt{\mathrm{6}}\:\leqslant\:\mathrm{x}\:\leqslant\:\sqrt{\mathrm{6}} \…