Category: Algebra

Question Number 27000 by abdo imad last updated on 01/Jan/18 $$Pisapolynomialhavngnroots{\left(x_i\right)}_{1⩽i⩽n}with{x}_i\ne x_{j}fori\ne j$$$${find}\:{the}\:{values}\:{of}\:\sum_{{k}\mathrm{1}} ^{{k}={n}} \frac{\mathrm{1}}{{x}−{x}_{{k}} }\:\:{and}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{\left({x}−{x}_{{k}} \right)^{\mathrm{2}} }\:. \…

Question Number 26999 by abdo imad last updated on 01/Jan/18 $$calculate\prod _{k=1}^{n}cos\left(\frac{a}{2^k}\right)and0<a<\pi thenfindthevalueof$$$${lim}_{n->\propto }\sum _{k=1}^{n}ln\left(cos\left(\frac{a}{2^k}\right)\right).$$ Answered by prakash…

Question Number 26998 by abdo imad last updated on 01/Jan/18 $$smlifyX=\prod _{p=2}^n\frac{p^3-1}{p^3+1}byusing1,j,j^{2}andj=e^{\frac{i2\pi }{3}}.$$ Terms of Service Privacy Policy Contact:…

Question Number 158065 by zainaltanjung last updated on 30/Oct/21 Answered by Rasheed.Sindhi last updated on 30/Oct/21 $$\sqrt{2+2\sqrt{\frac{3}{4}}}$$$$=\sqrt{2+\sqrt{3}}=p+q\sqrt{3}$$$$=2+\sqrt{3}=p^2+3q^2+2pq\sqrt{3}$$$$\:\:\:\:{p}^{\mathrm{2}}…

Question Number 158039 by HongKing last updated on 30/Oct/21 $$\mathrm{f}\left(\frac{\mathrm{x}+1}{2}\right)=\mathrm{x}+2\Rightarrow \mathrm{f}\left(\mathrm{x}\right)=?$$ Answered by puissant last updated on 30/Oct/21 $$y=\frac{x+1}{2}\to x=2y-1$$$$\Rightarrow f\left(x\right)=(2x-1)+2=2x+1$$ Answered…