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if-a-b-c-d-e-f-gt-0-and-abcdef-1-then-1-1-ad-1-1-be-1-1-cf-3-2-Profosed-by-Craciun-Georg

Question Number 221233 by Nicholas666 last updated on 28/May/25 $$ \\ $$$$\:\mathrm{if}\:{a},{b},{c},{d},{e},{f}\:>\:\mathrm{0}\:\mathrm{and}\:{abcdef}\:=\:\mathrm{1}\:, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{then} \\ $$$$\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{ad}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{be}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{cf}}}\:\leqslant\:\frac{\mathrm{3}}{\:\sqrt{\mathrm{2}}}\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Profosed}\:\mathrm{by}\:\mathrm{Craciun}\:\mathrm{Georghe} \\ $$ Commented by Rasheed.Sindhi…

let-0-a-b-c-2-and-a-b-c-3-Prove-that-3-2-1-a-1-1-b-1-1-c-1-11-6-

Question Number 221234 by Nicholas666 last updated on 28/May/25 $$ \\ $$$$\:\:\mathrm{let}\:\mathrm{0}\:\leqslant\:{a},{b},{c},\:\leqslant\:\mathrm{2}\:,\:\mathrm{and}\:{a}\:+\:{b}\:+\:{c}\:=\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}; \\ $$$$\:\:\frac{\mathrm{3}}{\mathrm{2}}\:\leqslant\:\frac{\mathrm{1}}{{a}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{{b}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{{c}\:+\mathrm{1}\:}\:\leqslant\:\frac{\mathrm{11}}{\mathrm{6}} \\ $$$$ \\ $$ Commented by Frix last updated…

Let-X-be-a-point-inside-a-square-ABCD-such-that-XA-10-cm-XB-6-cm-and-XC-14-cm-Find-the-area-of-the-square-

Question Number 221255 by MATHEMATICSAM last updated on 28/May/25 $$\mathrm{Let}\:\mathrm{X}\:\mathrm{be}\:\mathrm{a}\:\mathrm{point}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{square}\:\mathrm{ABCD},\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{XA}\:=\:\mathrm{10}\:\mathrm{cm},\:\mathrm{XB}\:=\:\mathrm{6}\:\mathrm{cm}\:\mathrm{and} \\ $$$$\mathrm{XC}\:=\:\mathrm{14}\:\mathrm{cm}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}. \\ $$ Commented by mr W last updated on 28/May/25 $${see}\:{also}\:{Q}\mathrm{72294}…

prove-Contour-integral-repreasentation-p-q-1-2pii-C-1-z-p-z-q-dz-z-

Question Number 221129 by SdC355 last updated on 25/May/25 $$\mathrm{prove} \\ $$$$\mathrm{Contour}\:\mathrm{integral}\:\mathrm{repreasentation} \\ $$$$\begin{pmatrix}{{p}}\\{{q}}\end{pmatrix}=\frac{\mathrm{1}}{\mathrm{2}\pi\boldsymbol{{i}}}\:\oint_{\:{C}} \:\left(\mathrm{1}−{z}\right)^{{p}} {z}^{−{q}} \:\frac{\mathrm{d}{z}}{{z}} \\ $$ Answered by MrGaster last updated on…

for-all-m-n-p-R-g-m-n-g-n-m-p-2-perfect-square-number-find-function-g-N-N-

Question Number 221081 by SdC355 last updated on 24/May/25 $$\mathrm{for}\:\mathrm{all}\:{m},{n},{p}\in\mathbb{R} \\ $$$$\left(\mathrm{g}\left({m}\right)+{n}\right)\left(\mathrm{g}\left({n}\right)+{m}\right)={p}^{\mathrm{2}} \left(\mathrm{perfect}\:\mathrm{square}\:\mathrm{number}\right) \\ $$$$\mathrm{find}\:\mathrm{function}\:\mathrm{g};\mathbb{N}\rightarrow\mathbb{N} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Complex-integral-1-dz-z-2-1-2-e-ipit-t-2-1-dt-3-C-1-z-dz-C-x-2-y-2-1-

Question Number 221095 by SdC355 last updated on 24/May/25 $$\mathrm{Complex}\:\mathrm{integral} \\ $$$$\mathrm{1}.\:\int_{−\infty} ^{\:+\infty} \:\:\:\frac{\mathrm{d}{z}}{\left({z}^{\mathrm{2}} +\mathrm{1}\right)^{\nu} }=?? \\ $$$$\mathrm{2}.\:\int_{−\infty} ^{+\infty} \:\:\frac{{e}^{\boldsymbol{{i}}\pi{t}} }{{t}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{t}=?? \\ $$$$\mathrm{3}.\:\oint_{\:{C}} \:\frac{\mathrm{1}}{{z}}\:\mathrm{d}{z}=??\:,\:{C};{x}^{\mathrm{2}}…

prove-P-d-dt-f-t-2-d-dt-g-t-2-dt-P-C-1-f-1-t-C-2-g-1-t-C-1-2-C-2-2-dt-

Question Number 221036 by SdC355 last updated on 23/May/25 $$\mathrm{prove} \\ $$$$\int_{{P}\in\left[\epsilon,\epsilon+\delta\right]} \sqrt{\left(\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}{f}\left({t}\right)\right)^{\mathrm{2}} +\left(\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}\mathrm{g}\left({t}\right)\right)^{\mathrm{2}} }\:\mathrm{d}{t}\leq\int_{{P}\in\left[\epsilon,\epsilon+\delta\right]} \:\frac{{C}_{\mathrm{1}} {f}^{\left(\mathrm{1}\right)} \left({t}\right)+{C}_{\mathrm{2}} \mathrm{g}^{\left(\mathrm{1}\right)} \left({t}\right)}{\:\sqrt{{C}_{\mathrm{1}} ^{\mathrm{2}} +{C}_{\mathrm{2}} ^{\mathrm{2}} }}\:\mathrm{d}{t} \\…