Category: Algebra

Question Number 146964 by mathdanisur last updated on 16/Jul/21 $$Simplify:$$$$\frac{\sqrt{2}\cdot \sqrt{2+\sqrt{2}}\cdot \sqrt{2-\sqrt{2}}}{\sqrt{2\sqrt{2}}}=?$$ Answered by Olaf_Thorendsen last updated on 16/Jul/21 $$x=\frac{\sqrt{2}\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2}}}{\sqrt{2\sqrt{2}}}$$$${x}\:=\:\frac{\sqrt{\mathrm{2}}\sqrt{\left(\mathrm{2}+\sqrt{\mathrm{2}}\right)\left(\mathrm{2}−\sqrt{\mathrm{2}}\right)}}{\:\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}} \…

Question Number 146960 by mathdanisur last updated on 16/Jul/21 Answered by TheHoneyCat last updated on 16/Jul/21 $$\mathrm{let}\mathcal{A}\mathrm{be}\mathrm{the}\mathrm{fuction}\mathrm{that}\mathrm{gives}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{surface}$$$$\mathrm{let}\mathrm{\Delta }=ABO$$$$\mathrm{let}x\mathrm{be}\mathrm{the}\mathrm{hatched}\mathrm{area}$$$$\mathrm{let}D\mathrm{be}\mathrm{the}\mathrm{intersection}\mathrm{between}\left[\mathrm{AO}\right]\mathrm{and}\mathrm{the}\mathrm{circle}\mathcal{C}(O,OR)$$$$\mathrm{let}\:{y}\:\mathrm{be}\:\mathrm{the}\:\mathrm{portion}\:{AOD}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}…

Question Number 146943 by mathdanisur last updated on 16/Jul/21 $$b_{\mathit{n}+2}\cdot b_{\mathit{n}+3}\cdot b_{\mathit{n}+4}=3^{3\mathit{n}+3}$$$$geometricseries{\mathit{b}}_8=?$$ Answered by Olaf_Thorendsen last updated on 16/Jul/21…

Question Number 15865 by prakash jain last updated on 14/Jun/17 $$a,b,c\in {\mathbb{R}}^{+}\mathrm{andIf}a+b+c=18\mathrm{then}\mathrm{maximum}\mathrm{value}$$$$\mathrm{of}{a}^2{b}^3{c}^4\mathrm{is}$$ Answered by Tinkutara last updated on…

Question Number 146914 by mathdanisur last updated on 16/Jul/21 $$\mid x^2-3x-4\mid =\mid x-4\mid \Rightarrow x=?$$ Answered by liberty last updated on 16/Jul/21 $$\mid a\mid =\mid b\mid \iff (a+b)(a-b)=0$$$$\Rightarrow\left({x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}+{x}−\mathrm{4}\right)\left({x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}−{x}+\mathrm{4}\right)=\mathrm{0}…