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Category: Arithmetic

Question-46814

Question Number 46814 by peter frank last updated on 31/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Nov/18 $${cos}\theta=\frac{{OP}^{\mathrm{2}} +{OQ}^{\mathrm{2}} −{PQ}^{\mathrm{2}} }{\mathrm{2}×{OP}×{OQ}} \\ $$$$\:\:\:=\frac{\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)+\left({c}^{\mathrm{2}}…

an-early-question-for-the-new-year-how-many-rectangular-triangles-with-sides-a-b-c-N-exist-with-one-side-2019-

Question Number 46809 by MJS last updated on 31/Oct/18 $$\mathrm{an}\:\mathrm{early}\:\mathrm{question}\:\mathrm{for}\:\mathrm{the}\:\mathrm{new}\:\mathrm{year} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{rectangular}\:\mathrm{triangles}\:\mathrm{with}\:\mathrm{sides} \\ $$$${a},\:{b},\:{c}\:\in\mathbb{N}^{\bigstar} \:\mathrm{exist}\:\mathrm{with}\:\mathrm{one}\:\mathrm{side}\:=\mathrm{2019} \\ $$ Answered by MrW3 last updated on 02/Nov/18 $${a}^{\mathrm{2}}…

Question-46686

Question Number 46686 by peter frank last updated on 30/Oct/18 Commented by peter frank last updated on 30/Oct/18 $$\mathrm{ABCDEFGH}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cube}.\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{projections}\:\mathrm{of} \\ $$$$\left.\mathrm{a}\right)\mathrm{AF}\:\mathrm{on}\:\:\mathrm{ABCD} \\ $$$$\left.\mathrm{b}\right)\mathrm{AG}\:\mathrm{on}\:\mathrm{ABCD}…

If-a-b-ab-4-1-then-a-b-a-gt-b-

Question Number 177648 by BaliramKumar last updated on 07/Oct/22 $${If}\:\:\frac{{a}\:+\:{b}}{\:\sqrt{{ab}}}\:=\:\frac{\mathrm{4}}{\mathrm{1}}\:{then}\:\:\:\:{a}\::\:{b}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:{a}>{b}\:\right] \\ $$ Answered by Rasheed.Sindhi last updated on 07/Oct/22 $${a}+{b}=\mathrm{4}\sqrt{{ab}}\: \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{16}{ab}−\mathrm{2}{ab}=\mathrm{14}{ab} \\…