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Category: Algebra

if-x-0-pi-2-then-prove-that-2-1-cotx-tan-3-x-cot-3-x-1-tanx-1-cotx-3-2-

Question Number 155776 by mathdanisur last updated on 04/Oct/21 $$\mathrm{if}\:\:\:\mathrm{x}\in\left(\mathrm{0};\frac{\pi}{\mathrm{2}}\right)\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{2}\:+\:\left(\mathrm{1}+\mathrm{cot}\boldsymbol{\mathrm{x}}\right)\left(\mathrm{tan}^{\mathrm{3}} \boldsymbol{\mathrm{x}}+\mathrm{cot}^{\mathrm{3}} \boldsymbol{\mathrm{x}}\right)}{\left(\mathrm{1}+\mathrm{tan}\boldsymbol{\mathrm{x}}\right)\left(\mathrm{1}+\mathrm{cot}\boldsymbol{\mathrm{x}}\right)}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

if-x-y-gt-0-then-prove-that-x-2-1-xy-2-x-2-y-4-1-x-2-1-y-2-1-xy-x-2-y-xy-2-3xy-

Question Number 155774 by mathdanisur last updated on 04/Oct/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y}>\mathrm{0}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{xy}\right)^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{4}} \left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} +\left(\mathrm{1}+\mathrm{y}\right)^{\mathrm{2}} }{\mathrm{1}\:+\:\mathrm{xy}\:+\:\mathrm{x}^{\mathrm{2}} \mathrm{y}\:+\:\mathrm{xy}^{\mathrm{2}} }\:\geqslant\:\mathrm{3xy} \\ $$ Terms of Service…

x-y-z-4-z-t-x-3-y-z-t-4-t-x-y-1-find-the-value-of-x-2-y-2-z-2-t-2-

Question Number 90225 by jagoll last updated on 22/Apr/20 $$\mathrm{x}+\mathrm{y}+\mathrm{z}\:=\:\mathrm{4} \\ $$$$\mathrm{z}+\mathrm{t}+\mathrm{x}\:=\:−\mathrm{3} \\ $$$$\mathrm{y}+\mathrm{z}+\mathrm{t}\:=\:\mathrm{4} \\ $$$$\mathrm{t}+\mathrm{x}+\mathrm{y}\:=\:\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} \: \\ $$ Commented…

k-1-n-k-4k-2-1-2k-3-

Question Number 155745 by cortano last updated on 04/Oct/21 $$\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left(\frac{\mathrm{k}}{\left(\mathrm{4k}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{2k}+\mathrm{3}\right)}\right)=? \\ $$ Answered by amin96 last updated on 04/Oct/21 $$\underbrace{\frac{{a}}{\mathrm{2}{k}−\underset{\mathrm{4}{k}^{\mathrm{2}} +\mathrm{8}{k}+\mathrm{3}} {\mathrm{1}}}}+\underset{\mathrm{4}{k}^{\mathrm{2}}…

A-a-b-IR-2-a-2-b-2-1-prove-that-A-can-t-be-written-as-the-cartesian-product-of-two-parts-of-IR-

Question Number 155729 by henderson last updated on 03/Oct/21 $$\mathrm{A}=\left\{\left({a},{b}\right)\in\mathrm{IR}^{\mathrm{2}} \:/\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} \leqslant\mathrm{1}\right\} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{A}\:\mathrm{can}'\mathrm{t}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{the}\:\mathrm{cartesian} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{two}\:\mathrm{parts}\:\mathrm{of}\:\mathrm{IR}. \\ $$ Answered by Kamel last updated on…