Question Number 35297 by 123 45 polytechnicien last updated on 17/May/18 $${sokve}\:{x}^{\mathrm{3}} +\mathrm{6}{y}^{\mathrm{3}} =\mathrm{4}{z}^{\mathrm{3}} \:{x}\:{y}\:{z}\:{integers} \\ $$ Commented by Rasheed.Sindhi last updated on 18/May/18 $$\mathrm{4z}^{\mathrm{3}}…
Question Number 166346 by LEKOUMA last updated on 18/Feb/22 $$\int\frac{{dx}}{\mathrm{1}+\sqrt{{x}}+\sqrt{\mathrm{1}+{x}}} \\ $$ Commented by mkam last updated on 18/Feb/22 $$\boldsymbol{{w}}\:=\:\mathrm{1}\:+\:\sqrt{\boldsymbol{{x}}}\:+\sqrt{\mathrm{1}+\boldsymbol{{x}}}\:\Rightarrow\:\boldsymbol{{dw}}\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}\sqrt{\boldsymbol{{x}}}\:+\mathrm{2}\sqrt{\mathrm{1}+\boldsymbol{{x}}}}\right)\boldsymbol{{dx}} \\ $$$$ \\ $$$$\Rightarrow\:\boldsymbol{{dw}}\:=\:\left(\:\frac{\mathrm{1}}{\mathrm{2}\:\boldsymbol{{w}}\:−\:\mathrm{2}}\:\right)\:\boldsymbol{{dx}}\:\Rightarrow\:\boldsymbol{{dw}}\:\left(\:\mathrm{2}\:\boldsymbol{{w}}\:−\:\mathrm{2}\:\right)\:=\:\boldsymbol{{dx}} \\…
Question Number 100785 by 175 last updated on 28/Jun/20 Answered by john santu last updated on 28/Jun/20 $$\mathrm{consider}\:\mathrm{m}\:\leqslant\:\sqrt[{\mathrm{3}\:}]{\:\mathrm{n}}\:\leqslant\:\mathrm{m}+\mathrm{1} \\ $$$$\mathrm{m}^{\mathrm{3}} \:\leqslant\:\mathrm{n}\:\leqslant\mathrm{m}^{\mathrm{3}} +\mathrm{3m}^{\mathrm{2}} +\mathrm{1}\: \\ $$$$\underset{\mathrm{n}\:=\:\mathrm{1}}…
Question Number 35244 by JOHNMASANJA last updated on 17/May/18 $${if}\:\:{y}=\frac{{sin}^{−\mathrm{1}} {x}}{\mathrm{1}−{x}^{\mathrm{2}} }\:\:{show}\:{that}\: \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}}\:−{xy}=\mathrm{1} \\ $$ Commented by math1967 last updated on 17/May/18 $$\left(\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 166301 by LEKOUMA last updated on 18/Feb/22 $$\int\frac{{x}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +\sqrt{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }}}{dx} \\ $$ Answered by MJS_new last updated on 18/Feb/22 $$\int\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}+\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}}…
Question Number 100744 by Dwaipayan Shikari last updated on 28/Jun/20 $$\mathrm{Happy}\:\boldsymbol{\mathrm{tau}}\:\boldsymbol{\mathrm{day}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{all}}\:!!! \\ $$$$ \\ $$$$\mathrm{28}\:{june}\: \\ $$ Commented by Dwaipayan Shikari last updated on 28/Jun/20…
Question Number 35208 by Rio Mike last updated on 16/May/18 $${The}\:{points}\:{A},{B},{C}\:{have}\:{coordinates} \\ $$$$\left(\mathrm{3},\mathrm{1}\right),\left(\mathrm{1},\mathrm{5}\right),\left(\mathrm{5},\mathrm{7}\right) \\ $$$$\left.{a}\right)\:{find}\:{the}\:{line}\:{l}_{\mathrm{1}} \:{joining}\:{the}\:{points} \\ $$$${A}\:{and}\:{B} \\ $$$$\left.{b}\right){Find}\:{the}\:{line}\:{l}_{\mathrm{2}} \:{perpendicular} \\ $$$${to}\:{l}_{\mathrm{1}} \:{and}\:{passes}\:{through}\:{the}\:{point} \\…
Question Number 100624 by Dwaipayan Shikari last updated on 27/Jun/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}}…\infty\:\mathrm{using}\:\mathrm{cos}\:\mathrm{function} \\ $$ Commented by MJS last updated on 27/Jun/20 $$\mathrm{why}\:\mathrm{cos}? \\ $$$${x}=\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}….}}}} \\ $$$${x}^{\mathrm{2}}…
Question Number 35088 by Raj Singh last updated on 15/May/18 $$\boldsymbol{{a}}\:\boldsymbol{{son}}\:\boldsymbol{{and}}\:\boldsymbol{{father}}\:\boldsymbol{{do}}\:\boldsymbol{{a}}\:\boldsymbol{{work}}\:\boldsymbol{{in}} \\ $$$$\mathrm{24}\:\boldsymbol{{day}}\:.\:\boldsymbol{{if}}\:\boldsymbol{{both}}\:\boldsymbol{{work}}\:\boldsymbol{{together}} \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{father}}\:\boldsymbol{{work}}\:\boldsymbol{{last}}\:\mathrm{6}\:\boldsymbol{{day}}\:\boldsymbol{{only}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{they}}\:\boldsymbol{{how}}\:\boldsymbol{{much}}\:\boldsymbol{{do}} \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 100539 by Dwaipayan Shikari last updated on 27/Jun/20 $$\left(−\mathrm{1}\right)^{{n}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{3}^{{n}} }{{n}} \\ $$ Commented by maths mind last updated on 27/Jun/20…