Category: Algebra

Question Number 27449 by rohith siddharth last updated on 07/Jan/18 $$factorise{a}^4-{(b+c)}^4$$ Answered by $@ty@mlastupdatedon07/Jan/18$$Letb+c=d$$$${a}^{\mathrm{4}} −{d}^{\mathrm{4}}…

Question Number 158508 by HongKing last updated on 05/Nov/21 $$\mathrm{if}\mathrm{x};\mathrm{y};\mathrm{z}>0\mathrm{and}\mathrm{xyz}=27\mathrm{prove}\mathrm{that}:$$$$\frac{1}{{\mathrm{x}}^2+27}+\frac{1}{{\mathrm{y}}^2+27}+\frac{1}{{\mathrm{z}}^2+27}⩽\frac{1}{12}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 158482 by HongKing last updated on 04/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 158465 by HongKing last updated on 04/Nov/21 Answered by qaz last updated on 04/Nov/21 $$\underset{\mathrm{n}=0}{\sum ^{\mathrm{\infty }}}\frac{\left(\begin{array}{c}2\mathrm{n}\\ \mathrm{n}\end{array}\right)}{4^{\mathrm{n}}(4\mathrm{n}+5)(2\mathrm{n}+2)}$$$$=\frac{\mathrm{1}}{\mathrm{2}}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}$$\left(\begin{array}{c}-1/2\\ \mathrm{n}\end{array}\right)$$\left(−\mathrm{1}\right)^{\mathrm{n}} \left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}−\frac{\mathrm{4}}{\mathrm{4n}+\mathrm{5}}\right)…

Question Number 27382 by abdo imad last updated on 05/Jan/18 $$resolveinsideC{\left(\frac{z-i}{z+i}\right)}^n+{\left(\frac{z+i}{z-i}\right)}^n=2cos\theta and0<\theta <\pi .ninteger.$$ Answered by sma3l2996 last updated on 05/Jan/18 $$\left(\frac{{z}−{i}}{{z}+{i}}\right)^{{n}} +\left(\frac{{z}−{i}}{{z}+{i}}\right)^{−{n}} −\mathrm{2}{cos}\theta=\mathrm{0}…