Category: Algebra

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

Question Number 158508 by HongKing last updated on 05/Nov/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{xyz}=\mathrm{27}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{27}}\:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} +\mathrm{27}}\:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} +\mathrm{27}}\:\leqslant\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$ 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 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\begin{pmatrix}{\mathrm{2n}}\\{\:\:\mathrm{n}}\end{pmatrix}}{\mathrm{4}^{\mathrm{n}} \left(\mathrm{4n}+\mathrm{5}\right)\left(\mathrm{2n}+\mathrm{2}\right)} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{−\mathrm{1}/\mathrm{2}}\\{\:\:\:\:\:\mathrm{n}}\end{pmatrix}\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 $${resolve}\:{inside}\:{C}\:\:\left(\frac{{z}−{i}}{{z}+{i}}\right)^{{n}} +\left(\frac{{z}+{i}}{{z}−{i}}\right)^{{n}} =\:\mathrm{2}{cos}\theta\:{and}\mathrm{0}\:<\theta<\pi\:.{n}\:{integer}. \\ $$ 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}…