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2-X-5-2-9-X-2-X-X-3-25-3-X-22-X-22-3-6-Z-63-1-20-6-Z-1-20-63-6-Z-44-Z-44-6-22-3-

Question Number 52653 by abdullahnewton last updated on 10/Jan/19 $$\mathrm{2}\:{X}\:\:+\:\:\mathrm{5}\:^{\mathrm{2}\:} \:\:=\:\:\:\:\sqrt{\mathrm{9}}\:\:\:\:−\:\:\:{X} \\ $$$$\mathrm{2}\:\:{X}\:\:\:+\:\:\:{X}\:\:\:=\:\:\:\mathrm{3}\:\:\:−\:\:\:\mathrm{25} \\ $$$$\mathrm{3}\:\:{X}\:\:\:=\:\:\:−\:\mathrm{22} \\ $$$${X}\:\:=\:\:\frac{\mathrm{22}}{\mathrm{3}} \\ $$$$ \\ $$$$\mathrm{6}\:{Z}\:\:−\:\mathrm{63}\:\:=\:\:\mathrm{1}\:\:−\:\:\mid\:\:\:−\:\:\mathrm{20}\:\:\mid \\ $$$$\mathrm{6}\:{Z}\:\:=\:\:\mathrm{1}\:\:−\:\:\mathrm{20}\:\:+\:\:\mathrm{63} \\ $$$$\mathrm{6}\:\:{Z}\:\:=\:\:\mathrm{44}…

Question-52630

Question Number 52630 by tanmay.chaudhury50@gmail.com last updated on 10/Jan/19 Commented by Kunal12588 last updated on 10/Jan/19 $${there}\:{also}\:{a}\:{movie}\:{named}\:{The}\:{Man}\:{Who}\:{Knew} \\ $$$${Infinity}\:\:{based}\:{on}\:{Mr}\:{S}.\:{Ramanujan} \\ $$ Commented by tanmay.chaudhury50@gmail.com last…

1-1-3-dx-x-2-x-2-1-2x-x-2-1-1-x-1-sinpix-1-dx-3-0-2-x-x-2-1-dx-4-0-1-e-2x-2x-d-x-x-5-2-3-x-2-5x-6-dx-from-question-1-to-4-greatest-integer-fuction-

Question Number 52619 by tanmay.chaudhury50@gmail.com last updated on 10/Jan/19 $$\left.\mathrm{1}\right)\int_{\mathrm{1}} ^{\mathrm{3}} \frac{{dx}}{{x}^{\mathrm{2}} +\left[{x}\right]^{\mathrm{2}} +\mathrm{1}−\mathrm{2}{x}\left[{x}\right]} \\ $$$$\left.\mathrm{2}\right)\int_{−\mathrm{1}} ^{\mathrm{1}} \left[{x}\left[\mathrm{1}+{sin}\pi{x}\right]+\mathrm{1}\right]{dx} \\ $$$$\left.\mathrm{3}\right)\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\left[{x}^{\mathrm{2}} +\mathrm{1}\right]} {dx} \\…

If-w-is-one-of-the-complex-cube-roots-of-unity-show-that-a-wb-w-2-c-a-w-2-b-wc-is-equal-to-2-b-2-c-2-ab-bc-c-Kindly-help-me-out-Thank-you-

Question Number 183667 by Mastermind last updated on 28/Dec/22 $$\mathrm{If}\:\mathrm{w}\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{cube}\: \\ $$$$\mathrm{roots}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{a}+\mathrm{wb}+\mathrm{w}^{\mathrm{2}} \mathrm{c}\right)\left(\mathrm{a}+\mathrm{w}^{\mathrm{2}} \mathrm{b}+\mathrm{wc}\right)\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\left(\alpha^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{ab}−\mathrm{bc}−\mathrm{c}\alpha\right). \\ $$$$ \\ $$$$…