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Author: Tinku Tara

A-triangle-with-perimeter-7-has-integer-side-lengths-What-is-the-maximum-possible-area-of-such-a-triangle-

Question Number 19330 by Tinkutara last updated on 09/Aug/17 $$\mathrm{A}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{perimeter}\:\mathrm{7}\:\mathrm{has}\:\mathrm{integer} \\ $$$$\mathrm{side}\:\mathrm{lengths}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{possible}\:\mathrm{area}\:\mathrm{of}\:\mathrm{such}\:\mathrm{a}\:\mathrm{triangle}? \\ $$ Answered by mrW1 last updated on 09/Aug/17 $$\mathrm{3}/\mathrm{3}/\mathrm{1}\Rightarrow\mathrm{A}=\sqrt{\mathrm{3}.\mathrm{5}×\mathrm{0}.\mathrm{5}×\mathrm{0}.\mathrm{5}×\mathrm{2}.\mathrm{5}}=\mathrm{1}.\mathrm{479} \\…

Solve-the-equation-y-3-x-3-8x-2-6x-8-for-positive-integers-x-and-y-

Question Number 19329 by Tinkutara last updated on 09/Aug/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:{y}^{\mathrm{3}} \:=\:{x}^{\mathrm{3}} \:+\:\mathrm{8}{x}^{\mathrm{2}} \:−\:\mathrm{6}{x}\:+\:\mathrm{8} \\ $$$$\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}\:{x}\:\mathrm{and}\:{y}. \\ $$ Commented by Tinkutara last updated on 12/Aug/17 $$\mathrm{RMO}\:\mathrm{2000}…

For-m-1-0-x-ln-m-x-e-x-1-2-ln-m-3-

Question Number 150402 by mathdanisur last updated on 12/Aug/21 $$\mathrm{For}\:\:\mathrm{m}\geqslant\mathrm{1} \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{x}\:\mathrm{ln}^{\boldsymbol{\mathrm{m}}} \:\left(\mathrm{x}\right)}{\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{1}}\:=\:\mathrm{2}\:\mathrm{ln}^{\boldsymbol{\mathrm{m}}} \:\boldsymbol{\zeta}\left(\mathrm{3}\right) \\ $$ Commented by yadiirama last updated on…

tan-1-x-x-1-x-3-2-

Question Number 19326 by priyankavarma094@gmail.com last updated on 09/Aug/17 $$\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{x}}−\mathrm{x}/\mathrm{1}+\mathrm{x}^{\mathrm{3}/\mathrm{2}} \right) \\ $$ Commented by NEC last updated on 09/Aug/17 $${please}\:{if}\:{you}\:{need}\:{any}\:{calculation} \\ $$$${let}\:{us}\:{know}.{Stop}\:{writing}\:{phrasal} \\…