Category: Algebra

Question Number 183846 by Michaelfaraday last updated on 30/Dec/22 Answered by MJS_new last updated on 31/Dec/22 $$1.x=0\Rightarrow \sqrt{x-\sqrt{x}}=0$$$$2.x>0$$$$t=\sqrt{x-\sqrt{x}}⩾0\Rightarrow x=\frac{{(1\pm \sqrt{4t^2+1})}^2}{4}$$$$\mathrm{insert}\:\mathrm{in}\:\mathrm{the}\:\mathrm{given}\:\mathrm{equation}\:\mathrm{to}\:\mathrm{get}…

Question Number 118298 by hmh2k20 last updated on 16/Oct/20 $$\mathrm{b},\mathrm{x},\mathrm{y},\mathrm{c}\mathrm{are}\mathrm{consecutive}\mathrm{terms}\mathrm{of}\mathrm{a}\mathrm{G}.\mathrm{P}.$$$$\therefore \mathbf{x}=\mathbf{br},\mathbf{y}={\mathbf{br}}^2,\mathbf{c}={\mathbf{br}}^3$$$$$$$$\mathrm{A}.\mathrm{M}.\mathrm{between}\mathrm{b}\mathrm{and}\mathrm{c}\mathrm{is}\mathrm{a}$$$$\therefore \frac{\mathrm{b}+\mathrm{c}}{2}=\mathrm{a}\Rightarrow 2\mathbf{a}=\mathbf{b}+\mathbf{c}$$$$$$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\boldsymbol{\mathrm{a}}\mathrm{bc}\:=\:\left(\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\right)\mathrm{bc} \…

Question Number 183825 by Michaelfaraday last updated on 30/Dec/22 $$solveforxbyusinglambertfunction$$$$2^x+3x=8$$ Answered by MJS_new last updated on 30/Dec/22 $$\mathrm{generally}$$$${b}^{{x}}…

Question Number 118280 by hmh2k20 last updated on 16/Oct/20 $$\left(26\right)\overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{a}}=\left(\begin{array}{c}4.8\\ 3.6\end{array}\right),\overrightarrow{\mathrm{OB}}=\overrightarrow{\mathrm{b}}=\left(\begin{array}{c}8\\ 15\end{array}\right)$$$$\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}=(4.8)\left(8\right)+(3.6)\left(15\right)=92.\overrightarrow{4}$$$$\mathrm{a}=\sqrt{4.8^2+3.6^2}=\sqrt{23.04+12.96}=\sqrt{36}=6$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}\:=\:\sqrt{\mathrm{8}^{\mathrm{2}}…

Question Number 118275 by bramlexs22 last updated on 16/Oct/20 Commented by bramlexs22 last updated on 16/Oct/20 $$f\left(x\right)=x^2,when$$$$(\frac{3}{f\left(1\right)f\left(2\right)}+\frac{5}{f\left(2\right)f\left(3\right)}+\frac{7}{f\left(3\right)f\left(4\right)}+\frac{9}{f\left(4\right)f\left(5\right)}+\frac{11}{f\left(5\right)f\left(6\right)}).x<70$$$$Findthelargestcomplete$$$${solution}\:{of}\:{the}\:{inequality}\:. \…