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Let-a-b-R-Show-that-a-b-a-b-

Question Number 1543 by 112358 last updated on 17/Aug/15 $${Let}\:{a},\:{b}\in\mathbb{R}.\:{Show}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid\mid{a}\mid−\mid{b}\mid\mid\leqslant\mid{a}−{b}\mid. \\ $$ Answered by Rasheed Soomro last updated on 18/Aug/15 $$\boldsymbol{\mathrm{Alternative}}\:\boldsymbol{\mathrm{way}}\:,\:\boldsymbol{\mathrm{technically}}\:\boldsymbol{\mathrm{simpler}}. \\ $$$$\mid\mid{a}\mid−\mid{b}\mid\mid\leqslant\mid{a}−{b}\mid………………….\left(\boldsymbol{\mathrm{I}}\right)…

sin-1-xdx-

Question Number 132613 by aurpeyz last updated on 15/Feb/21 $$\int{sin}^{−\mathrm{1}} {xdx} \\ $$ Answered by Dwaipayan Shikari last updated on 15/Feb/21 $${xsin}^{−\mathrm{1}} {x}−\int\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\…

x-2-0-

Question Number 1545 by x-2 last updated on 17/Aug/15 $${x}−\mathrm{2}=\mathrm{0} \\ $$ Answered by 123456 last updated on 17/Aug/15 $${x}−\mathrm{2}=\mathrm{0} \\ $$$${x}−\mathrm{2}+\mathrm{2}=\mathrm{0}+\mathrm{2} \\ $$$${x}=\mathrm{2} \\…

Find-n-1-1-2n-1-4-

Question Number 1539 by 314159 last updated on 17/Aug/15 $$\boldsymbol{\mathrm{Find}}\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}\right)^{\mathrm{4}} }. \\ $$ Answered by 123456 last updated on 17/Aug/15 $$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{4}}…

Question-132597

Question Number 132597 by Study last updated on 15/Feb/21 Commented by mr W last updated on 15/Feb/21 $$\frac{\mathrm{156}}{{x}+\mathrm{7}}=\frac{\mathrm{156}}{{x}}−\mathrm{14} \\ $$$$\mathrm{156}{x}=\mathrm{156}\left({x}+\mathrm{7}\right)−\mathrm{14}{x}\left({x}+\mathrm{7}\right) \\ $$$${x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{78}=\mathrm{0} \\ $$$$\left({x}−\mathrm{6}\right)\left({x}+\mathrm{13}\right)=\mathrm{0}…

Question-132594

Question Number 132594 by Study last updated on 15/Feb/21 Commented by mr W last updated on 15/Feb/21 $${the}\:{sum}\:{of}\:{two}\:{complex}\:{numbers} \\ $$$${can}\:{be}\:{a}\:{real}\:{number},\:{e}.{g}.\: \\ $$$$\left(\mathrm{1}+{i}\right)+\left(\mathrm{1}−{i}\right)=\mathrm{2} \\ $$$${the}\:{product}\:{of}\:{two}\:{complex}\:{numbers} \\…