Category: Algebra

Question Number 52108 by ajfour last updated on 03/Jan/19 Answered by mr W last updated on 03/Jan/19 $$Area=\frac{cR}{2}=\frac{\sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}}{4}$$$$\Rightarrow R=\frac{\sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}}{2c}$$ Commented by ajfour…

Question Number 52087 by prakash jain last updated on 03/Jan/19 $$\mathrm{If}1,a_1,a_2,\dots ,a_{n-1}\mathrm{are}{n}^{th}\mathrm{roots}\mathrm{of}$$$$\mathrm{unity}\mathrm{the}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}$$$$\frac{1}{1+1}+\frac{1}{1+a_1}+\frac{1}{1+a_2}+..+\frac{1}{1+a_{n-1}}$$$${n}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{number} \…

Question Number 117603 by Ar Brandon last updated on 12/Oct/20 $$\mathrm{Let}\mathrm{f}:\mathbb{R}\to \mathbb{R}\mathrm{be}\mathrm{a}\mathrm{function}\mathrm{satisfying}\mathrm{the}\mathrm{following}:$$$$\left(\mathrm{a}\right)f(-x)=-f\left(x\right)$$$$\left(\mathrm{b}\right)f(x+1)=f\left(x\right)+1$$$$\left(\mathrm{c}\right)f\left(\frac{1}{x}\right)=\frac{f\left(x\right)}{x^2}\mathrm{for}\mathrm{all}x\ne 0$$$$\mathrm{Show}\mathrm{that}$$$$\left(\mathrm{i}\right)f\left(x\right)=x\mathrm{for}\mathrm{all}x,\mathrm{y}\in \mathbb{R}$$$$\left(\mathrm{ii}\right)\:{f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left(\mathrm{y}\right)\:\mathrm{for}\:\mathrm{all}\:{x},\mathrm{y}\in\mathbb{R} \…

Question Number 183118 by leicianocosta last updated on 20/Dec/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 183084 by Rasheed.Sindhi last updated on 19/Dec/22 Commented by JDamian last updated on 19/Dec/22 $$SameQ182973$$$$Infactyouwrotedownthesolution$$ Commented by Rasheed.Sindhi last…